Just after some thoughts.
My C64C i got some time ago (as DOA) is well still DOA

Powered it up with known good PSU. grey screen. nothing much else. RAM chips hot as hell. shut off. desoldered them (known issue as they fail)
Started buzzing out the traces to make sure everything is ok. +5VDC and GND have continuity. WTF?
Most of the chips on the c64c are soldered on board (minus 2) - i've removed them and still same, short somewhere.
Don't know if another chip has shorted, or, whats going on .... could always plug back it now the RAM chips are gone and see what gets hot next, but, nah, not really.