Whats the absolute cheapest way to fix my very old very dead amp?
Replace the guts with a circuit board from a solid-state no-name amp from E-Bay. Leaving the filament circuit connected (so the tubes will still glow) would cost extra and you did say “cheapest”. The point is that bringing basket cases back to life can be very difficult and expensive, particularly if the transformers are dead, the parts are obscure, the schematic is unavailable, and/or the tubes required are unobtainium. If the amp is broken to the point where the fix exceeds the value of the amp, sometimes you just have to accept it and move on. Unless it is particularly valuable as a collector piece or already working, that garage sale amp is very likely to be a false bargain. If cost is your primary concern, go buy something inexpensive that comes with a warranty.