If you never changed out the PSU it is possible the PSU is going bad, I would try several things first.
1) Determine when this started happening?
2) How long does it take to lock up from the initial start-up?
3) Does it stay up longer if you dont do anythiong and let the computer just sit there?
4) When was the last time you did anything to change the configuration of your system? to include hardware and software?
Any of things things could cause your problem... if it is a heat issue, then anytime you run extra programs, it will lock up... an easy way to test that theory is to simply open one side of your case, if it doesnt lock up, then it might need a new layer of thermal paste, or your CPU fan could be going bad.
If it was a config change, then remove the hardware or software which changed and see oif the problem persists...
write back soon, and let us know how it goes....