My computer will work fine all day long and other times it will shutdown randomly. When I go to turn it on again nothing happens, I have to turn the power of at the wall a once or twice and then when I turn it on it powers up and works properly again. Is this a problem with my computer's power supply? I have ran all kinds of diagnostic software and nothing seems to be wrong with anything in my system.

check all the connections first and make sure its all secure if it is, try swap the power supply, your power supply might be overloading.. how many device you have in your computer?

Check out your CPU temperature; hopefully your BIOS will register the temperature in "Health" section. What you are experiencing is typical of overheating. Also check that none of your fans, including the Power Supply fan, are failing and losing RPMs. If any fan is making a noise it never used to, check it out.

To the first response: All the connections are secure, and I don't have a large number of devices on my computer. the only extra devices I really use are a burner, an active USB port. My modem has it's own power supply. How do I find out the capacity of my power supply? The second response: My CPU temperature is pretty good and hovers below 50c at worst. CPU fan is running at just above 4500 rpm Will check out the power supply fan, is there a good utility for this? At the moment I am using a evaluation version of SISoftware Sandra.

There is no utility that I know of to check PS fan RPMs. The thing to do is play a video game that is demanding for an hour and then immediately check your CPU temp. Next - it could be your power supply, like others have said. That fact that your unit crashes and you have to turn it off&on couple of times tells me PS. Sometimes it has to cool down a little before it starts again - connection problem internally.