Interesting question: if piggybacking really does work, why don't those will little soldering skill simply attach a ram chip on top of the broken one?

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That would work. You'd want to do a little bit of soldering on all the pins to be sure they didn't let go over time. But if you're in there, fixin' stuff... why not do it right and put in a socket? Besides, one failed. Likely others will follow. If you fix one - you might as well fix them all.