A bit of research suggests it may be a ROM chip, RAM problems or the POKEY sound chip not functioning. It does not help you very much, but may serve as a starting point for further research.
You ideally want to pull them out before pushing them down. You don't necessarily have to remove them completely; just wiggling them out a little is often enough to redistribute any oxide or corrosion that may have built up, which can cause a bad connection. If the pins look particularly dull, a quick clean up with fine sand paper can also work wonders.Yes, first step should be to open the machine up and press down on all socketed chips to make sure they are firmly seated in the sockets.
Depends - what kind of RAM chips does it use and how many? It's unlikely you'd have to replace them all though. You may be able to spot a shorted chip by leaving the machine on for a few minutes and checking if any are running hot (watch you don't burn your fingers!). After replacing any hot chips, swap the rest out one by one to see if that makes any difference....any idea where I can get a set of RAM chips for that unit cheap?