From that, first things first is to open the side while its running, take a look at the fan, if its spinning, thats one of the list of possible problems. Take a nice visual check of how much dust is in there and also capacitors and other components. If you deem to need a better inspection, turn the computer off, leave everything plugged into the wall etc as normal, just switch the wall plug off, shouldn't get any shocks then
Monitoring temperature is an easy thing to do. You may even feel something is not right if the air temperature in your room has increased a lot.
Download this - http://www.almico.com/sfdownload.php
This will tell you all your system temperatures. Says my graphics card is running at just below 60 degrees, which is alright
Not enough power.. shouldn't be that, its been alright for the past few years
See what happens there, also check all cables are in securely, if one of them pops out the screen effectively 'turns off' as it detects its not being used so it turns off to save power
