My system fan failed a few days ago. I noticed this when the alarms started going off before a very abrupt shutdown. Now very little works like it should. This is the 2nd time I've badly overheated this due to faulty fans (first time cost me a better CPU). Currently, the system will load up, will run for a while with few problems (aside from a locked keyboard) and can run some applications. Given the circumstances, I strongly suspect something (CPU, mobo, or mem) is burnt out. How can I determine which? I'd rather not yet invest in a new CPU/mobo if I don't have to.

CPU: Athlon XP1500+ not overclocked
Motherboard: Gigabyte GA-7VAX
Memory: 2 x 256MB DDR
Video card: Radeon x700 pro
OS: WinXP sp2

symptoms:
- keyboard locked up, even at bootup, replugging might fix briefly
- occasional beeps from internal speaker, sometimes persistent
- Gigabyte's overclocking app reports CPU temp at approx. 50°C and system temp at a frosty 0°C (BIOS reports correctly)
- sound may be corrupted by loud white noise
- system shuts itself off as opposed to normal crash/reset

This page has memory testing under DOS: http://www.benchmarkhq.ru/english.html?/be_memory.html At the top of the page is click on CPU to get those tests for the CPU. Boot your machine under DOS - meaning that you will need to make a bootable A:\ floppy.

However, the primary suspect is your power supply.

easytune4, the overclock app that came with my board shows the power supply as putting out:
Vcore: 1.74V
+3.3V: 3.24 (+1.8%)
+5V: 4.27 (-17%)
+12V: 12.54 (+4.5%)
+5Vsb: 4.89 (-2.2%)

most look ok, but that 5V supply looks exceedingly low
what's the usual acceptable operating ranges for this?
i read somewhere that it was supposed to be ±5%

As a rule of thumb, you want + voltages to stick within +-5% of the rated amount.

+12V: +11.40 to +12.60
+5V: +4.75 to +5.25
+3.3V: +3.14 to +3.47