It sounds like you have electrical problems under control.
Just in case here's the programming info. I've never tried it as my fobs still work after 9 years with just a battery change and one re solder job like you need.
1) Enter vehicle and close all doors.
2) Fasten seat belt so as to cancel the chime. Turn the ignition to the "ON" position.
3) Press and hold the UNLOCK button on the programmed fob for 4 seconds. Within 6 seconds with the UNLOCK button still depressed, press the PANIC button. WHen a single chime is heard, release both buttons. The chime indicates the system is in the program mode.
4) Press and release both the LOCK and UNLOCK buttons simultaneously on the fob to be programmed. A single chime will be heard. This indicates the fob has been recognized.
5) Within 4 seconds of hearing the chime, press and release the LOCK and UNLOCK button and the fob being programmed. A single chime will be heard. This indicates the fob has been programmed.
6) Repeat steps 4 and 5 up to a total of 4 fobs. 7) Turn the ignition OFF.
8) Cycle the ignition or wait 60 seconds. Within this time, the vehicle will exit the program mode, and all fobs should function normally.
NOTE: When entering the program mode using a programmed fob, ALL currently programmed fobs will be erased and will have to be programmed for the vehicle. If the program mode is entered and no action is performed, the previously programmed fobs will continue to function.