Computer Wont start, eventhough fans/disk/power all runs?

My PC was turning off a few times and wouldn't start up till you unplugged the Power cord and pluged it back in, The PC would do this 2 to 3 times a week, over a ~2 month period. Though it was power supply problem. But recently my PC started doing this again, and I would turn on My PC, and I would hear all fans/Dist drive work, and all lights on. I was able to starrt up the PC about 2 times with me having to restart my PC about 10-20 times b4 it went through and Actually STARTED the program. And on my third shut off the System wont start up, even though all lights/fans/ ect are running. I did replace the power supply, but that didnt resolve the issue. Can anyone theorize what can my problem be?