Have you tried dismantling the entire machine - remove the keyboard, mouse, floppy, any HDs, etc. Does the machine have a chipRAM expansion board? Remove it too.
See if that boots up.
Then try taking the KS out, and see if that will boot up with a coloured error screen.
Take the whole motherboard out of the metal shielding and check whether there's any damage to the traces on the underside (this may be a bit tedious, as you've got to unfasten all of the hexnuts at the back...)
Apply pressure to each of the main chips - I know that they're surface mounted, but there may be a bad connection.
Leave it switched on without doing anything for about 30-60 minutes. See if any of the components get warm - or hot (I don't think that there's anything in the standard A600 that gets hot to touch; that may indicate a problem).
Can't think of anything else...
