Thanks everybody for the suggestions; I'll try them later after I let the Macintosh LC sit for a while.
However, I'm suspecting it's the PSU. D: It can't be the monitor, as the hard drive doesn't spin up.

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Sounds like you might have to try what Byrd said. I tried that once with the LC II we've talked about, but it didn't work. I just left it on and plugged in for a while until it actually booted up on its own. It seems that it doesn't like to be out of power for very long periods of time (I'm talking like months).