FYI for anyone who may ever care, dead key fob battery or not, you are never dead in the water. For either the C6 or the C7, you can use the key contained inside your key fob (oh yes there is), open the rear hatch with it (yes... there's a key slot above the licence plate, near the release button). With the hatch open, pull the little tab that has the wire attached, located on the left inside side panel. That opens the drivers door. Get in (through the now open driver's door) and insert the key fob into the slot GM was nice enough to design just for this purpose. In the C6, the slot is in the glove box. In the C7 the slot is on the right side of the steering column. For the C6, insert the fob in the slot with the buttons facing the passenger side. For the C7, insert with the buttons facing upward. Your computer will now recognize the key fob and you can start your car.
If you did not know this, or in addition wouldn't know how to get out of your car if you're inside and the door buttons didn't work for any reason, then while you have the glove box open, it might be a good idea for a refresher read through the owner's manual. If you have never read through your owner's manual, or maybe took it out of the glove box to make room for your gloves, or used it to start a campfire one night, or you just can't be bothered, well... good travels and I hope you never end up in either of these predicaments...