Is it possible for a computer to use AC power?
Computers represent everything with bits, and ordinarily this means one voltage range for a 0 and another voltage range for a 1. If you really wanted to use AC to in some way directly represent bits, you wouldn't be able to rely on voltage in the usual way, since by definition AC voltage is always changing.

You could play games with phase or frequency though. Consider using phase. You could define a 'reference' phase with some oscillator, and then a 0 could be AC with phase matching the reference, and 1 would be AC that's 180 degrees out of phase. (or vice versa) But right away you should see the problem even with this: while you can tell what the state of a DC bit is practically instantly, with these hypothetical AC bits, you'd have to wait a significant portion of a cycle to tell what sort of bit you had. So you'd have to run your reference phase at a very high frequency to get even mediocre performance. If you tried to use different frequencies for bits, the situation would be as bad or worse.

It would be interesting to try to get a couple of logic gates implemented this way, but only as an academic curiosity.