I can think of two (non-destructive) ways. If your car has fold down rear seat backs, you might be able to squeeze in there with a flashlight and see how to get the trunk open. This may or may not be feasible.
The other way is to call a locksmith. He can get the trunk open and come up with a key or a new lock/key combo. It will cost you about $40 unless you have a AAA (or anyone else's) auto club membership, in which case, you're probably covered.
FriPilot
split the fob halfs and the battery will be on the backside of the board!
Try looking in the trunk on the driver's side inside fender underneath the carpeting.
can i used jadoo without remote
You'll have to get a tuner to disable it through the computer. If your talking with a remote start, you can bypass it with a "passlock" which can be found at car alarm shops
buy a universal remote.
buy a universal control
Mine has died too. I looked around on line to see what was available. There are lots of places that will sell you an exact replacement. They run about $50. Check GOOGLE for "key fobs" FriPilot
How to program a keyless entry remote for 2008 Pontiac g5
A remote control is used to control an electronic device form a distance without wires. It uses infrared or radio frequencies to transmit the data to the device.
With a key (especially if the remote is on the fritz)
The ORIGINAL Idiot Box!
How to program a keyless entry remote for 2008 pontiac g5