I am not familiar with the circuitry on the 520. However, there are Mac logic boards (IIci, e.g.) which will not activate the power supply if certain capacitors have failed.

Also, leaked goo from the capacitors can be extremely difficult to see and may cause shorts (mildly conductive goo) or opens (corrosive goo eats away traces, solder, pins and vias) on the logic board.

The first thing I would try is to give the logic board a good washing (several methods recommended in threads at these fora). If that doesn't work, then try replacing the remaining capacitors.

If that doesn't work, decide whether you want to try to trouble shoot it to a lower level.