Computer intermittently shuts down

im sorry, I'm not usually one to do this, but I have searched everywhere without a solution, and I'm flabbergasted. My computer sometimes shuts down immediately after turning it on, and it sometimes takes a minute or two. If I run it in safe mode, (if I can get to the point where I CAN run it in safe mode) it works fine, but any time I try to start it up normally, even if I don't even log into windows and just let it sit on the login screen, it shuts off after a short amount of time. I assumed the problem was the case fan since it had been making loud noises recently, and that didn't solve it. I went into safe mode thinking it could be malware or a virus and ran both malwarebytes and roguekiller, which both found many problems, deleted all of the problems found, and still the same problem. I'm not sure if maybe it's the power supply, but I just replaced that about 6 months ago and the fan inside of it seems to be working perfectly. I'm not sure what else to try, please, any direction would help very much. I'm running an HP Pavillion p6210f with Windows 7