Commodore 64 Repair

While I wait for parts for my recalcitrant ZX Spectrum, I turned my attention to a sick Commodore 64 bread bin model 250407 that I picked up from a friend. As with the ZX, this C64 doesn’t boot at all. No black screen with the white line on the left, just… nothing.
At least this C64 does not look like it had any work done internally. The soldering on the bottom looks factory, and there’s no messy flux residues. Both the SID and VIC chips are socketed, but I think this generation all came this way.
I have a loaned power supply for this board, which is a dodgy original outputting 10.6VAC on the 9VAC line, and +5.2V on the 5V DC line. Not great, not terrible, and it’s definitely going to be replaced with a modern version down the line. For now, and for testing, it will do…