Remove ram, take logic board, and wash it well, soaking it for a good, long time, followed by rinsing. Possibly even scrubbing lightly with a clean toothbrush where the goo from leaking capacitors may be bridging chip connections might help. I have also occasionally rubbed very carefully with ethyl alcohol, which seems to remove the most persistent goo from between chip connectors.

Let it dry for several days, or a day in a soft breeze if you are in a warm climate, reinstall the board, turn the machine on, and see if this improves matters. Soldering may not be required (for now).

The capacitors on the logic board are mostly those little silver/ aluminum coloured "tanks". There are maybe 12-15 of them, and they come in a number of sizes. They have lettering on them such as "20µF 5v" and other such specifications.

The washing/ scrubbing approach described just revived a CII that was given to me as scrap, which is nice, as I have wanted one for years.