bigmessowires said:

Edit: sorry, that link is for the PSU itself, not the startup circuit on the logic board. I can't seem to find a reference to the technique now, but I think it involved a jumper wire from the logic board battery to somewhere in that circuit. Maybe someone else will remember what I'm talking about.

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I remember what  you're writing about, but not where an explanation of the technique is.

I just wanted to jump in and mention that if those caps have failed, still replace all the electrolytic caps on the board.   The power supply issue is the canary for the rest of the caps.  

Trying to figure out which vias or traces were eaten by capacitor goo is not fun, so best to deal with it sooner than later.   Well, somebody probably thinks it's fun, but for most people it's kind of tedious, I think.