2005 G6 remote . lock won't work but unlock does. Does not seem to be battery. Maybe the connection inside ?

With a voltage meter see how many volts are at the starter terminal. If not 12+ volts you have a bad connection. Check connection at the starter solenoid. Does it have 12+volts? Short the solenoid. Does it put voltage to the starter?

May have lost the program,

Change the battery in the remote key.

What kind of vehicle is it?

Try changing the battery inside the remote usually that solves the problem but otherwise u might also have broken or loose parts inside the remote from dropping it on the ground,or rubber gasket maybe in in perfectly, if none of those solutions work, it may need to be reprogrammed or replaced,from the dealership.
usually its the coin cell battery eg:2016,2032,etc
and u'll need a small flat precision screwdriver and some patience when opening it.

When you press the trunk open button, do you hear any "release" noise come from the trunk area? The issue may be a bad battery in the key fob OR there could be an issue with the transmitter located inside the vehicle. Do the doors lock and unlock properly? is the vehicle equipped with security or immobilizer? please advise

Are you talking about the car battery? or the remote battery?

change the battery in the remote.the nearer the car you have to get the lower the battery power.

new battery and probably the remote cleaned out

Replace battery first and see if that help, if not then follow steps below, if you cant figure it out or it still doesn't work, or take it to the dealer, it could be remote module is faulty. Keep the windows open as a safety measure, then,

Remove the ignition key from the ignition lock cylinder.

Remove the BCM PRGRM fuse from the fuse panel. Refer to Fuse Block 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, & then back to ACC within 1 second.

Open & 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 & hold the transmitter LOCK & 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 Fuse Block in Wiring Systems.