Your comment about only being able to drive 30 miles per hour but the engine is revving at 5000 RPM leads me to believe you have a transmission problem and the transmission is going into limp mode. That means the transmission is locked into 2nd or 3rd gear (not sure which on the 05 Cobalt) so you can drive the car some place to have the transmission serviced. The TC light might only be a symptom of the transmission problem, not a problem in itself. Is your cousin knowledgeable about transmissions? Can he (did he) scan for trouble codes?
I think you need a transmission rebuild, but course I could be completely wrong, and someone else might chime in with an easy fix for a common condition on the 05 Cobalt.