Yes I had this happen. The alarm is not GM so they won't touch it at all especially since its a Best Buy install. If they reprogrammed your keys(key in this instance), whatever key or universal key hidden inside your dash to use the aftermarket remote start no longer works. If I can explain it right, the car remote starts because it thinks a key is in the car already. Usually you have a 3rd valet key inside a box or a blank key coded to your working keys and that is used to start the car. I had a spare key cut and not programmed on purpose so if anyone stole my key they had to figure out it only works if you started the car from remote start. If not it was just gonna turn the radio on and unlock the steering column.
The stolen key can still unlock the door handle but I doubt they are gonna manually key each handle of a Chevy hoping to find yours. When you place registration in glove box does it have your address? in Ohio, they give us a restricted copy with no address for that reason and never store your real home address in any GPS. Use the gas station or police station near the freeway so the directions point you near your neighborhood. You should be able to get home from the freeway exit by now unless you just moved 2 weeks ago.
What year and trim do you have? Not sure if losing the key would turn off Cruise Control. You can also contact Chevy Customer care about that issue but the remote start one may be a up hill battle but you are in a better place than I was. I had a bricked ECU in my Subaru and the dealership wanted me to tow my car to Best Buy to valet mode my car before they would run tests and still couldn't figure out I had a bricked ECU from the error codes on the cluster after that was done.