Does it have soft-power? If so, you might want to check if something is shorting out the power on pins on the ADB port. This could be something as simple as the power key being stuck down on the keyboard. Try plugging it in without any ADB devices plugged in - does it still boot? If it does, then check the motherboard around the ADB ports for any shorts.

If it looks clean, or the PSU doesn't support soft-power, then you might want to try unplugging the PSU from the motherboard and any drives, and try plugging the bear PSU into the mains. If it still turns on by itself then there's probably something wrong with it. So I'd try a new PSU!