don't know if the game has a test mode, but garbled screen usually means the CPU is not executing anything which could mean any of the following (assuming power is already checked)
system clock circuitry not working- often the case easy to check rudimentry with a logic probe or look to see if the cyrstal is broken, often they are missing entirely on the old boards
CPU bad - replace with another to see if there is a change
ROM bad - easy to check if you have a ROM burner, though vary rarely "the problem" in my experience
RAM bad - common fault, not easy to check without a fluke but if the system has only a few RAMS, can shotgun replace.
any of the circuitry dealing with the address decoder or address bus - common but, very hard to check without more advanced equipment (like a fluke), schematics, logic probe and understanding of digital logic and basic CPU architecture.
-brian