Macintosh LC takes forever to boot

So I have a Macintosh LC III (in an LC II case) that takes about 10 to 20 minutes to power up and boot.  Once it does, it seems to work fine, but if it goes more than a few hours without a power on, it just sits there spinning its fan for an increasingly extended period with nothing on the screen.  I've tested the monitor with my DuoDock and it seems to work fine, so I know it's the computer.  I'm guessing that it's a failing capacitor, the question is which one?