Here are a few simple, non-soldering things to try before setting it aside for another day. From the photo, the board looks relatively clean, but certainly dusty. It might benefit from a thorough and careful clean.

Also, the error message may or may not be correct. The self-test is necessarily somewhat crude, and it can be confounded by other problems. Even though the message indicates a RAM problem, it nonetheless may be worthwhile reseating the ROM chips. Carefully lift them out of their sockets, and then push them gently (but firmly) back into place. Over time, the contacting surfaces oxidize, and a little abrasion restores good contact.

Finally, measure the supply voltages (the floppy connector on the back provides convenient access to all voltages of interest). If they are more than 5% off of nominal, that could be a source of trouble. If they are more than 10% off of nominal, that's almost certainly a problem.