Bad Memory Card? or Power Supply?

I'm using Windows XP on a Dell Dimension 2350. I have to leave the PC on full time now because I have trouble restarting the PC.
When the PC is turned OFF and I push the Power ON button the PC appears to be booting up but then appears to be going on and off by itself. With the side panel removed I can see that the fan is turning off and on. I can get the PC to boot up and work only if I turn it on and off a dozen or more times. So I now just leave it on full time.
I tried to replace the 2 memory cards with one new 512MB card but that did not solve the problem as the problem persisted. I tried removing one and then the other of the 2 memory cards and that did not help.
Somebody has now told me that it may be a power supply problem.
Advice PLEASE!

 

The only way to know for sure is to put a new PS in and try it! You can get some good ones for around $30 bucks - http://www.newegg.com