I'm now running memtest86 over the 24G of memory in case the problem is there. So far, it has made seven complete passes without detecting anything. I will let it go until it says it has completed a full test sequence, but I'll be surprised if it finds anything now. If it's not memory, it's a bit hard to guess where the problem is. Since we never get as far as writing on a disk, it's not going to be there. Nor do we use the network.
The machine is certainly almost OK. Maybe even quite OK. It certainly seems to run Linux as I'd expect, although I haven't attempted exhaustive tests yet. Testing is so slow and so boring and gets in the way of everything else I'd like to be doing. And it's Friday.
My spouse has decided that we need a weekend away in a luxurious place far from the normal world. This seems like an excellent plan. Maybe the computer will reveal something useful next week. I'll be running out of time to claim DOA status for the bits by then, so that might affect my sleep tonight. On the other hand, losing sleep over a box of bits is probably unwise. Consider this as a muted scream.