My computer keeps turning off randomly, but my monitor, speakers etc stay on. I have also been having problems with my monitor. She picture keeps going all fuzzy, lots of thin black lines moving around. HELP!

So the tower just shuts down? Loses all power? What exactly happens?

Is the computer old? Have you ever opened it and cleaned it out?

I think I have figured out that the CPU is getting way to hot. I checked the temp at start-up and it was about 53 degrees but it gets up to 92 degrees which I assume is what is making it automatically shut down. I opened it up and the fan attached to the cpu is moving, but very slowly. I am thinking that maybe it needs a new one but I have no idea how to go about fixing it.

You most likely need to change it.

You just need to get a Heatsink/Fan that is the same type as your CPU socket.

If you do not know what the socket type is then what is the motherboard make and model? This should be fairly plainly labeled on the board.

The manufacturer's web site will have the specs. Or is it a brand name comp such as Dell or HP etc.? If so they would have the specs.

Anyway just remove the old one and clean off the old thermal compound and apply a dab of new compound and the new heatsink/fan.

Most have fairly simple pins (usually 4) that twist in and out to remove and install.