If the power supply is not putting out the correct voltages, disk drives won't work, and the motherboard will be unreliable. Check the 12V and 5V supplies with a voltmeter. There is an adjustment on the analog board for output voltage which sets the 12V output. If the Mac is upgraded or has accessories plugged in, you may have to set 12V a bit high to bring 5V within range. 5V should read between 4.75 and 5.25 V, and 12V should be between 12 and 13V.

Have you checked that the disks you're using will boot another Mac? A bad disk is still the most likely culprit.