Why, After about 10min of driving my alero starts to skip, then shut off.

Well firestone did a diagnostic on it, would they not do that themselves during the diagnostic you think? And what do you think it is if it shuts off after and what do you think it is if it shuts off before?

Firestone said that my computer itself is not responding. It is giving off no codes that can be used to identify the problem. Is my only option to go to gm?

No you need a qualified technician, besides Firestone to find the issue. Firestone in your area apparently does not have a qualified person or experienced people to diagnose a drivability problem. The computer will not set a code if the fuel pump fails, and other drivability issues as well. The Technician has to find the problem, sounds like they are part changers.