Originally Posted by Evereddie
I'm 100 % sure you do not have enough power from that extension cord to make the AC run. You might have actually damaged the AC.
Sometimes you can get away with running the AC on 15 amp outlet if nothing else is drawing on that circuit, but it should trip the house breaker first. I wouldn't think its likely that this caused the issue.
OP didn't say if its brand new or if it was working before, but sounds like an issue with the AC. Thermostat seems to be calling for cool and the fan is running, so probably time for service on the AC.