quick question....

Several folks have mentioned the horrors of being aboard an airplane in the summer time w/o an operating APU.

Is this to say that the aircrafts air conditioning system cannot/is not run by the engines while the plane is on the ground?

I always thought that once the engines were running, power for the a/c systems came from that, and not necessarily the APU.

Obviously Im missing something here, guys. Heh.