I would start by isolating the tuner section entirely, seeing as it's basically useless these days.
Find the main driver chip, download a data sheet and find the composite video input pin.
Then trace it back to the input jack. Somewhere along the way it'll probably split off to the tuner section, usually through a switch or similar.
I've found that the manufacturers at least loosely follow the reference schematic in the data sheet (they are all pretty similar with the notch filters and stuff anyway) so it should be pretty easy to map the few caps, inductors and resistors between the input jack and driver chip.
Then just desolder the closest component to that split heading towards the tuner.
Once you have that isolated, you can start properly tracking down any other faults (like bad caps etc).
Can you take a few decent photos of both sides of the PCB and internal construction etc?