Cube starts up & shuts down on its own

I've got a G4 Cube, 400 mhz, 80 mb hd, 1 gb ram, OS 10.4.11.

It's recently developed this odd habit of periodically starting up for no reason at all. There's nothing anywhere near the power buttons on the cube or the display, you didn't touch it, you didn't touch the desk, the mouse, the light switch on the wall, nothing. And suddenly, bing, it's starting up.

Which isn't so terrible by itself. Spontaneous startups I could live with.

It's more the spontaneous shutdowns that annoy me. My wife will be checking email, visiting a website, whatever, and suddenly the computer just shuts down. Sometimes it shuts down, then starts up, then shuts down again just for kicks.

I've reset the PRAM, and that did nothing. I'm thinking I'll try resetting the PMU button on the board, but I'm wondering if anyone has an idea on what might be causing this.

The Cube has an unusual power button, as some of you know, so I'm guessing there might be something about the touch-sensitive variety that makes this sot of thing possible.

Anyway, any thoughts?

Thanks.