Are the fans running? If not, it's probably really a psu problem. I had a similar problem with one of my PCs once.... actually, I short circuited it since I have a bad habbit of working on the PC while it's running
ops: The built-in safety mechanism kicked in and I couldn't boot it up after the initial shutdown. Forgot how I got it running again, think I somehow reset the psu by messing with the switches. In your case, open up the case and check for bad wiring (melted, etc). You never know what've been damaged.
If you can't afford an expensive psu like the Antec, you can go for an enermax which is around $50. Right now, I'm running a CAD$30 Sparkle (oem) 300W silent psu on my athlon and it works very well. In fact, it's even more stable than my old 350W Antec SmartPower. The fans in my 1 yr old Antec are dying and noisy as hell. However, most generic psu are poorly built and will end up costing you more in the long run.