Here's what happens:

I hit the start button, and sometimes it'll go, sometimes it won't. When it won't, the dome light and the voltmeter shut off with what sounds like a clunk, as if the starter is about to go, or a relay switches on and gets stuck.

If I disconnect the battery and reconnect it, power is restored. A couple times, I just waited and the power eventually came back. However, waiting stopped working after the first couple times it happened.

One time, I was turning the nova around in the driveway, and it sounded like the starter engaged (a buzzing sound) and everything cut off, including the motor. I waited and the power eventually came back and I was able to resume turning the car around.

I checked the two wires going to the starter, they looked fine. Any other ideas where to look? I checked the voltage at the fuse box and they all read fine with the key on and off.

Sorta weird. If the switch and wiring is stock, a guess would be that the starter/sloenoid is binding up. That's the only thing that I can think of that may be a buzz or click sound.

if it bound up, would it buzz while running? the starter/solenoid are only a year old, could it be the alignment on the block? how do i check that?

I'm just guessing that the buzzing is coming from the starter. I can't hear it. This thread might help with a bind problem.
http://www.chevelles.com/forum/ultimatebb.php/topic/41/440.html

check all your cables from your battery, they may have gone bad or the connection might be just loose.

Clean the connections, regardless of how they look, with a brass brush or small wire brush at the battery terminal, the battery posts themselves, on the engine block for ground, and the terminals on the ends of the cables where they connect on the block and solenoid.

It is absolutely essential that these be clean beyond the point you would think. Also, if you have thin battery cables, and/or if you see any sign of green coloring on the wires inside the battery cable shielding, replace them with some decent thick cables. The bigger round the better.

Steve