CH - I would go for a memory problem first - as it is the easiest to cure, most likely etc.
Try this :
Pull your memory simms out (or unclip - whatever) and replace. If you have a pair or more, swap the positions around. Be sure to use the same motherboard slots though.
If this cures the problem, great - you just had a dirty / high resistance contact.
Whatever the outcome down load this memory test from :
Memtest
This produces a boot floppy and is totally independant of WINDows or whatever. Run this full cycle and it will tell all. In fact thinking about it - I would do this first.
The next place to look is your power supply. Local resources will vary, but if you are not upto a ps swap - I bet you know someone who is.
Hope this helps
MG