I upgraded my CPU from a celeron 3.4Ghz to a Core 2 Quad q6600. It booted okay and ran a lot faster but after 10 minutes it froze and I had to turn the power off to restart it. This happens all time runs great but only for 10 minutes. Cpu temp is only 34C. PSU is only 300W is this enough.
Is 300 W enough? It depends on your other components. However I wouldn't suspect power supply issues right away. First I'd like to know about your motherboard. Is the CPU on your motherboard's approved list? I ask because the computer presumably came with the Celeron and the mobo may not be able to handle a quad core.
Why don't you give us a more detailed list of components or a PC model number so we can diagnose more effectively. If you download CPU-z and run it you can gain alot of information about your motherboard, CPU, and ram.