The alarm system likely has a main wire from the battery to the system module. It will be smaller than the regular battery cables and probably hooked to the positive post .
There may be a series of wires so unhook them one at a time. When you unhook ( or cut ) the correct one, the alarm won't work anymore . You need to be aware though, some direct battery wires run other systems on the vehicle. If thats the case then you need to find and un hook the alarm module from 12 volt source at the module
SOURCE: Looking to disable the alarm system for a 1996 Jeep Cherokee Sport
you need to find out which wires go to what like the ones going into the alarm and the ones coming from the car u might have to put them back together..hopefully they are color coordinated for you good luck
SOURCE: 1996 Explorer anti-theft system won't disable
Try re-setting the computer...Disconnect the negative terminal of the battery and leave off for 5-10 minutes. This will allow the computer to reset. The charger may have interupted the signal or something.
SOURCE: Diagram of 1996 ford ranger fusebox which fuse is
RANGER FUSE PANEL
Fuse Position
Rating
Circuit Protected
1
7.5 Amp
Power Mirror
2
—
Not Used
3
15 Amp
Parking Lamps
4
10 Amp
Left Headlamp
5
10 Amp
On Board Diagnostic (OBD) II System
6
7.5 Amp
Air Bag System/Blower Relay
7
7.5 Amp
Illumination Switches
8
10 Amp
Right Headlamp/Fog Lamp System
9
10 Amp
ABS System
10
7.5 Amp
Speed Control/GEM System/Brake Interlock
11
7.5 Amp
Warning Lamps
12
10 Amp
Front Washer System
13
15 Amp
PCM System/Stoplamps/
4WD/ABS/Speed Control
14
10/20 Amp
ABS System
15
7.5 Amp
Air Bag System/Alternator
16
30 Amp
Front Wiper
17
15 Amp
Cigar Lighter
18
15 Amp
A/C System
19
25 Amp
Ignition Coil/PCM System
20
7.5 Amp
Radio/GEM System/Anti-Theft
21
15 Amp
Hazard Lamps
22
10 Amp
Turn Signals
23
—
Not Used
24
10 Amp
Starter Relay/Anti-Theft
25
7.5 Amp
Speedometer/GEM System
26
10 Amp
4R44E/4R55E Trans./Backup Lamps/DRL System
27
10 Amp
Underhood LP/Map Lights/Glove Box Lamp/Dome Lamp/Visor Lamps/4x4 Sys.
28
7.5 Amp
GEM System
29
10 Amp
Audio System
30
—
Not Used
31
—
Not Used
32
—
Not Used
33
15 Amp
High Beam Lamps
34
—
Not Used 
SOURCE: i have just charged the battery on my 1996 r reg
unlock the car with the key/hold over for 30 secs.
lock the car with the key/hold over 30 secs.
then press/hold down unlock button on remote.
you have just reset your alarm/central locking system
change remote batteries every 2 years...... both remotes....
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