Manual transmission Reverse cable is broken from main linkage housing. Connector for the reverse cable is plastic and cannot find where this section broke away from.

Check the linkage first. They put plastic grommets on the arms. They disintegrate. After that, it is internal. They also put plastic tabs on the shift forks. Could be a bad gear.

2004 doesn't have a modulator valve . An if it did it would affect all gear operation , Shift hard , but would still go into gear. You have an internal transmission problem !
No Reverse, Slips in Reverse
Checks
Causes
Reverse Clutch
No apply or slipping
Piston and Seal Assembly (457)
Binding, cracked, or leaking
Inner Seal (456)
Plugged orifice
Clutch Plates (460-463)
Worn friction or broken splines
Snap Ring (459, 464)
Out of position
Housing (454)
Cracked, plugged feed holes, or broken tangs
Housing Retainer and Ball Assembly
Missing or out of position
Springs (458)
Binding
Reverse Clutch Fluid Routing
Fluid leak or restriction
Driven Sprocket Support (95)
?€¢
Leaking seal rings

?€¢
Porosity, damage, misalignment

Channel Plate and Gasket, and Valve Body, Gaskets, and Channel Plate
Porosity, fluid leak across the channels, misalignment, damage, or fluid restriction
Low and Reverse Band and Servo
No apply or slipping
Servo Piston (69)
Broken or binding
Servo Piston Seals (71, 72)
Leaking
Servo Pin (67) and Springs (66, 68)
Binding
Servo Cover (73)
Broken, loose, or leaking
Low and Reverse Band (111)
Broken, worn, or out of position
Anchor Pin (64)
Broken
Fluid Feed Tubes (83)
?€¢
Broken, bent, or plugged

?€¢
Missing or leaking seal rings

Transmission Case (1)
Porosity, fluid leak, or restriction
Shift Linkage
Disconnected or misaligned
Manual Valve (800) and Link (802)
Disconnected or misaligned
#1 Checkball
Missing, no low band fluid
Fluid Level
Low
Fluid Pressure
Low
Refer to High or Low Line Pressure .
suggest you take to an ASE certified transmission repair facility !

Something in gear shift linkage broken or separated

There are several thing's that can cause a no reverse !
No Reverse, Slips in Reverse
Checks
Causes
Reverse Clutch
No apply or slipping
Piston and Seal Assembly (457)
Binding, cracked, or leaking
Inner Seal (456)
Plugged orifice
Clutch Plates (460-463)
Worn friction or broken splines
Snap Ring (459, 464)
Out of position
Housing (454)
Cracked, plugged feed holes, or broken tangs
Housing Retainer and Ball Assembly
Missing or out of position
Springs (458)
Binding
Reverse Clutch Fluid Routing
Fluid leak or restriction
Driven Sprocket Support (95)
?€¢
Leaking seal rings

?€¢
Porosity, damage, misalignment

Channel Plate and Gasket, and Valve Body, Gaskets, and Channel Plate
Porosity, fluid leak across the channels, misalignment, damage, or fluid restriction
Low and Reverse Band and Servo
No apply or slipping
Servo Piston (69)
Broken or binding
Servo Piston Seals (71, 72)
Leaking
Servo Pin (67) and Springs (66, 68)
Binding
Servo Cover (73)
Broken, loose, or leaking
Low and Reverse Band (111)
Broken, worn, or out of position
Anchor Pin (64)
Broken
Fluid Feed Tubes (83)
?€¢
Broken, bent, or plugged

?€¢
Missing or leaking seal rings

Transmission Case (1)
Porosity, fluid leak, or restriction
Shift Linkage
Disconnected or misaligned
Manual Valve (800) and Link (802)
Disconnected or misaligned
#1 Checkball
Missing, no low band fluid
Fluid Level
Low
Fluid Pressure
Low
Refer to High or Low Line Pressure .
Most likely your trans needs to be rebuilt !
to

It is probably not an adjustment issue. You probably have something broken or loose between the shift lever and the transmission. Look for a bad cable or housing or brackets broken near shifter. If it is floor shifted, it is possible that it has something broken in the shifter.

Probably just a little piece of plastic in the shift linkage has broken or fell out. Check all the linkage you can get at easily for loose connections, loose mounts, etc. This linkage goes all the way to the transmission, so you won't be able to see all of it.

bottom, but the manual mentions a couple different procedures. See below.

4.1L Engine

1. Before servicing the vehicle, refer to the Precautions section.
2. Remove or disconnect the following:
   
   Negative battery cable Steering gear and linkage assembly Harness connector Starter retainers Starter
   

To install:
Install or connect the following:

Starter Starter retainers. Tighten the starter retainers to 30-37 ft. lbs. (40-50 Nm). Harness connector Steering gear and linkage assembly Negative battery cable
Alternate procedure:

1. Remove or disconnect the following:
   
   Negative battery cable Engine undercover Harness connectors Starter motor mounting bolt and nut
   
2. Remove engine mounting insulator bottom nuts, and lift engine approximately 2 inches with a transmission jack
3. Remove starter motor

To install:

1. Installation is in reverse order of removal; observe torque values shown in diagram
   
   

Fig. Starter motor mounting and torque specifications-Q45 & 2004 M45

Sounds like a plastic grommet is broken. You'll have to raise the car and check the cables/linkage at each end. You'll probably find on one end that the grommet is missing. And you probably not be able to buy just the grommet. you will have to replace the entire cable.

Shift Control Linkage The transmission range selector control linkage consists of the following components:

• a floor mounted transmission range selector lever.
• a transmission control switch on the transmission range selector lever.
• a cable connecting the transmission range selector lever to the transmission manual control lever.
• a brake/shifter interlock system.
• an ignition/shifter interlock cable (3F719) connecting the reverse kick down spring (7219) to the steering column lock assembly.

-------------------------------------
Section 07-05: Transmission, Automatic—External Controls 1996 Mark VIII Workshop Manual
REMOVAL AND INSTALLATION Gearshift Lever Removal

1. Place transmission range selector lever in OVERDRIVE. Remove console finish panel (04567). Refer to Section 01-12 .
   

Console Panel, Floor Removal and Installation

1. Remove gearshift lever. Refer to Section 07-05 .
   
2. Remove center A/C-heater instrument panel finish panel (04338).
   
3. Remove instrument panel finish panel (044D70).
   
4. Remove two screws retaining console finish panel (04567) to radio control cover (04530).
   
5. Unsnap RH rear corner of console finish panel and then disengage three retaining clips from LH rear corner.
   
6. Disconnect cigar lighter socket and retainer (15055), lamp and switch connectors and remove console finish panel.
   
7. Remove two screws retaining console panel (045A36) to instrument panel (04320).
   
8. Open glove compartment door (06024) and remove console glove compartment mat (047A74) in bottom of console glove compartment (06010) to gain access to two console panel-to-instrument panel console bracket retaining screws. Remove screws.
   
9. To remove, slide console panel rearward and up.
   
10. To install, reverse Removal procedure. Tighten screws to 1.5-1.9 Nm (13-17 lb-in).
    
    
    Console Panel, Floor

Item Part Number Description 1 046A44 Radio Finish Panel Assy 2 047A74 Console Glove Compartment Mat 3 045A36 Console Panel 4 N804234-S36 Screw (2 Req'd) 5 N800322-S36 Screw (2 Req'd) 6 N805180-S58 Screw (2 Req'd) 7 N806577 Nut (2 Req'd) A — Tighten to 2.5-3.1 Nm (22-27 Lb-In)

1. Remove brake interlock cable and disconnect cable from range interlock cam.
   
2. Disconnect transmission range indicator lamp/TCS electrical connector.
   
3. Raise vehicle on hoist. Refer to Section 00-02 .
   
4. Remove range cable retaining nut from transmission bracket. Disconnect shift cable and bracket (7E395) from transmission control selector connecting rod adjustment stud (7B415).
   
5. Lower vehicle. Remove range selector lever and housing retaining bolts and remove gearshift lever (7210).
   

Installation

1. Install transmission range selector lever to front floor pan (11135) with retaining bolts. Tighten to 6-8 Nm (4-6 lb-ft).
   

1. Connect shift cable and bracket. Tighten retaining screw to 3-4 Nm (25-35 lb-in). Install retaining clip and connect transmission range indicator lamp wire.
   

1. Install console finish panel.
   

1. Place the transmission range selector lever in OVERDRIVE and apply a 1.4 kg (3 lb) rearward force to the lever.
   

1. Raise vehicle on hoist. Refer to Section 00-02 .
   

1. Connect theshift cable and bracket to the manual control lever (7A256) and transmission bracket. Make sure manual control lever is in OVERDRIVE and tighten nut at bracket to 13-25 Nm (10-18 lb-ft).
   

1. Lower vehicle and check range selector for proper operation.
   

There is a connector on the top of the manual transmission. It is close to the battery box. It should face forward, meaning you can detach the connector from the (reverse) sensor by pulling the connector towards the front of the car. A possible issue is that this connector has gotten dirty or is not making a good connection. Check out this connector first to see if it looks clean and in good shape. The connector only has 2 electrical connections, kind of like small spade terminals in the connector. Make sure they are clean and making good connection with the sensor on the top of the tranny.

It's also possible to remove the reverse sensor from the transmission. It's in a cylindrical black plastic housing tha covers the portion of the shift linkage that actually enters the transmission. The sensor itself is pretty rugged, but it's possible that this black plastic housing has come loose or dislodged.