Put new battery in your transmitter and try this process....
Transmitter Programming
If you lose a transmitter, program the old and new transmitter(s) into the remote control door lock receiver's memory. Up to 4 transmitters may be programmed.
Important
Once the remote control door lock receiver enters the programming/diagnostic mode, the programming of the first transmitter erases all previous transmitter programming information, requiring the programming of all transmitters.
Program only 1 vehicle remote control door lock receiver at a time. If more than 1 receiver is being programmed at the same time, it is possible that the same transmitter could be programmed to more than 1 remote control door lock receiver
Perform the following steps in order to program the transmitter:
Remove the ignition key from the ignition lock cylinder.
Remove the BCM PRGRM fuse from the fuse panel. Refer to Electrical Center Identification Views in Wiring Systems.
Close all of the doors.
Close the liftgate.
Turn the ignition lock cylinder to ACC.
Turn the ignition lock cylinder to OFF, and then back to ACC within 1 second.
Open and close any vehicle door. A chime will be heard when the system enters the BCM programming/diagnostic mode.
Important
After 7 seconds, a chime may be heard confirming successful synchronization. It is necessary to wait approximately 14 seconds for a second chime that will confirm successful programming.
Press and hold the transmitter LOCK and UNLOCK buttons simultaneously for 14 seconds.
Repeat the previous step on each additional transmitter to be programmed.
Remove the ignition key from the ignition lock cylinder.
Install the BCM PRGRM fuse back into the fuse panel. Refer to Electrical Center Identification Views in Wiring Systems.
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Document ID# 475561
1998 Pontiac Trans Sport