Have worked on a few of these, the most common failure is actually within the TTL logic, especially if the board is mostly Fujitsu TTLs, these are dropping like flies nowadays. They seem to lose internal connections to their pins, so if an output pin is disconnected it becomes floating, and if an input pin is lost the chip die isnt getting the correct inputs and appears to be doing the wrong thing based on the inputs that can be seen externally. The SRAM is usually Fujitsu MBMxxxx chips which are very robust and EPROM faults are quite rare. The gfx and sound data is held in mask ROMs which are also a common failure but as they do not contain executable code they would not stop the board booting.
Of course all of that is based on what is most likely, that doesnt mean much to a specific board tho.