How old is old? Just because there are fuses instead of circuit breakers doesn't mean that the wiring is necessarily dangerous. I think maybe you need to get an electrician or qualified electrical inspector into the building. All we can do...
A bit of a long shot here, but try removing the CPU and replacing it. This sounds a bit like a bad contact somewhere. Since you've had the RAM sticks in and out, it's probably not on the memory contacts, although it wouldn't hurt to pull them...
The CPU is a 9600K? I was going to say just drop in another two sticks and let them run at the slower speed, and then I saw "I don't want to fart around with it." For minimum farting-around, even if it's only potential farting-around, pull the...