At this stage, in order to eliminate every possibility, I suppose you should unseat the CPU and check it out for excess grease, obvious damage, and whatnot. Eliminate the CPU as a suspect, and you’re down to the motherboard.
I used a twofold approach with mine: first, I cleaned the pre-installed thermal grease off the stock heat sink, because I wanted to use my own grease. Some alcohol, some rubbing, and it was nice and clean. I then pre-treated the heat sink by putting a tiny amount of grease on it and spreading it with a stiff card, just to force grease into the scratches and surface faults; any excess was cleaned off. This is more or less like grouting tile: get it into the crevices, none left on the surface.
Then, the “grain of rice” method: put a blob of grease the size of a grain of rice on the center of the CPU and press down the heat sink to spread it, locking it into place. I had to kajigger the sink around a bit to get it locked, more than I would have liked, but it came out fine. The CPU has kept around ambient temperature ever since, usually about 21C.
The grease I’d paid extra for, by the way, was the much-lauded Arctic Silver 5. Gotta be careful not to spread it, because it contains tiny metal particles and thus can conduct electricity.
Oh, and once again, I don’t mean to insult you, but: you say you were down to one stick of RAM. You did double-check that you installed the right kind, and in the right configuration and slots, right? Some motherboards are really finicky about where the first stick of RAM should go. At least, unseat and reseat it, just to be sure.
Congrats on the rig!