Most desktops that come in for repair are pretty dirty, which is pretty typical. If your fans are working properly, they are bringing in lots of dust and grime.
We have replaced thousands of power supply’s in our 25 years of performing computer repair in Northern KY. First thing we do is see if the desktop has any power at all. We check to see if there are any lights or fans spinning.
When a desktop comes into our computer shop with the problem being there is nothing showing up on the screen, the first thing we check is the video card, if it is a video adapter that is not attached to the motherboard and can be replaced.