The driver's Multiplex Control System is a small computer that controls (among many other things) the dash lights brightness, ignition key interlock, shift interlock, and has a tie in to the brake light system and horn relay. It may be that this small computer malfunctioned and started the whole problem chain.
However, I note from the factory shop manual that if polarity is reversed on the shift interlock--it can be damaged. Reverse polarity will ruin the diode inside the shift interlock. This could have happened when you jumped the battery--a brief period of getting the cables and terminals mixed up could have done it.
Checking the shift lock solenoid can be done by removing the steering column upper cover. Disconnect the shift lock solenoid connector (2 terminals). Using long jumper wires, apply battery voltage to terminal 1 (yellow wire side) of the solenoid and ground terminal 2 (green wire side). Check that the shift lever can now be moved out of Park. NOTE: applying voltage in the opposite direction of that above will damage the diode in the solenoid and will probably ruin it. Remove your jumpers and shift back to park and check that the solenoid locks. If the solenoid does not work properly, it will need to be replaced. This involves removing the end of the transmission shift cable and is a complex job. Remember, no power to the solenoid equals a locked solenoid--it takes power to unlock it.
The Multiplex Control Unit has a self diagnostic feature which checks the computer itself and inputs to the computer. The computer check is called mode 1 and the input test is mode 2. The diagnostic trouble codes are outputted to the ignition key light and beeper.
To test, first confirm that all fuses are good, especially fuse 9 (10A) in the driver's under dash fuse box (left kick panel) and fuse 13 (7.5A) in the passenger's under dash fuse box (right kick panel). Then use a jumper wire (a wire with small alligator clips on each end works best) to jump the two leads of the multiplex test connector. (This is a light green 2 terminal connector dangling from the same wire bundle as the brake pedal switch connector.) Buckle the driver's seat belt (avoids nuisance beeps). Now turn the ignition switch to on. After about 5 seconds, the ignition key light should come on and the beeper should beep for 2 seconds then stop for .2 sec. then beep once for .2 seconds. This indicates that the system is in diagnostic mode 1.
If no diagnostic trouble codes (DTC's) are present, the key light and beeper will not blink/beep again. If there are codes: about one second after entering mode 1, the key light and beeper will indicate the DTC and repeat it every 3 seconds. If there are more than one, the system will indicate them in ascending order. The codes will be a light flash and beep so you will have to count the flashes/beeps to keep track. The codes range from 1 to 6. Code 3 (three flashes/beeps) indicates a problem with the multiplex control unit itself. Write back here for other codes or for questions about mode 2.
There is a plastic cover that pops off at the pivot end of the wiper arm. pulling up on this with a hook of some kind from the furthest end should release it. Under it you will find a nut that holds the wiper arm to the shaft. It's quite common for the nut to come loose and the shaft spins without moving the arm. Try tightening this nut (with the ignition on, be sure the wiper motor is off, then turn off ignition and put the wiper arm in the parked position). This is a common problem if you've ever tried to turn on the wiper when it was frozen to the glass.
Try putting the gear selector in the neutral position . park neutral safety switch . Wouldn't need reprogramming , if it did you wouldn't be able to do it . Dealer only . Your best bet mite be to take your vehicle to a qualified repair shop any way . Viewing wiring diagrams for the starter circuit an using a DMM - digital multi-meter to test B+ power & ground's is how to find a fix. Do you know what a wiring diagram is ? How automotive electrical circuit's work ? How to use a DMM.
Electric Testing Techniques You Need to Know
Free wiring diagrams here http://www.bbbind.com/free_tsb.html
Enter vehicle info. year , make , model an engine size . Under system click engine then under subsystem click starting . Click the search button then the blue link . Looking at the diagram i see the ignition switch supplying B+ voltage to the starter cut relay ! Do you know what a relay is ? If the B+ can't make it through the coil side of the relay to the park neutral switch to ground the relay will not energize an close the contacts an send B+ voltage to the starter solenoid . You can test at the relay for B+ control from the ignition switch . Video's on youtube on checking relay circuit's
Not sure where you are having the problem, but if you removed the bolts on one of your motor mounts and use a floor jack to move the motor around a little that may give you the room you need, Just be careful not to go to far and brake something like a wire etc, good luck.
