Oggers,
Sounds like you got a duff Memtest floppy. Try to see if you can boot to another DOS boot floppy (easy to make in XP).
Since Memtest is open source there are several versions. I always use
this one.
You are quite correct in that if you haven't changed your s/w & h/w config it'll either be malware or the big three (you only mentioned two)
MEMORY - HEAT - POWER
It could be your PSU is on the way out. If when it's working to spec and the +12V rail is 16 Amps or less it would be marginal for your system anyway.
Try a min power config of graphics card, one hard drive and one memory stick. Disconnect / remove everything else, pci cards, floppy, optical drive, peripherals etc.
If it then works, suspect your PSU. You could also look to see how much undervoltage/fluctuation you are getting in the bios or with a utility like Speedfan (Google for it).