Not the only answer here, but you could try taking the memory array out and replacing it again, I mean just putting it back again. It could be a bad contact there. If you have more than on memory array take each out in turn and try booting with the remaining one. You might find a faulty one that way. (Please switch off and unplug mains before poking about inside poota!) It sounds like the memory is struggling past the first test but then falling over in real use. If you have a friend with similar poota then swap memory arrays to see if fault transfers to another machine.
Intermittent faults and warmth related ones are notoriously hard to track down. Just when you think you have it licked, plop! It happens again. Good luck and avoid wearing synthetic garments or nylon carpets when handling memory chips, static electricity kills them.