To me from personal experiance in pc repairs it definately sounds like a power supply problems. For a P4 and athlons it recommended with athleast 300 watts power supply. Power supply are also design to Shut itself down when the load is to large on them to prevent damage to pc.
Check out this site:
http://www.pcguide.com/ts/x/comp/power.htm
Its an osome resource site for pc repair
I hope this helps!!
Protecteur