Don't know what's wrong with old PC

[i dont want a username]

Hello, my family has an old dell Inspiron 531 and it has stopped working again. The on board graphics broke so it has an nvidia 8300 gt I think (if I remember right) and a 350w jeantec power supply because that broke too. When it is turned on it works for about 5 minutes then blacks out and turns off. After this it won't turn on or will cut out in less than a second and won't turn on properly until the next day. I think something may be wrong with the power supply or the processor not conducting well because of old thermal compound, but I don't know what's wrong. My Dad wants me to fix it, but if I fix the wrong thing then money will have been wasted. Anyone got any ideas on what the problem might be?
Thanks in advance for any help.

 

[i dont want a username]

Just ran hwmonitor from Cupid and the CPU (which is an amd athlon 64 x2 5000+) is only at around 40 to 50 degrees. I hear they can take more but the computer wasn't really doing anything so maybe I should replace the thermal compound anyway. I also forgot to mention the PC has windows vista and there isnt any bod so maybe it's the processor. The 8300 gs also got to the mid 40's and low 50's so is that too hot when idle?. I think we need a new family PC but my Dad doesn't agree.

 

[C12Friedman]

From your description, I would suspect the power supply but... before you change that, look over the motherboard really well as explained in this guide
http://www.pcstats.com/articleview.cfm?articleID=195
since capacitors do wear out and that is an issue of it's own

 

[i dont want a username]

thanks for that it was the power supply. i tested it with my psu and got my dad to order a new one but didn't have time to post it on the forum.