about display problem, if you get the usual light blue & blue colors at start up, VIC is 99% ok, the problem might be one of the CIA chips or both (6526), or even a damaged RAM chip.
uhm.. just read your post again... So you have a functioning C64c with no sound? Check the fuse in the machine! Check the fuses in the powersupply, if it's the old model powersupply with fuses in them. Alternatively, try a different powersupply.
Oh, and the two remaining breadbins "power up" as they use to say in ebay ads, but the TV screen is just black.