I take it is out of warranty so Google this as what I write next is the usual.
"The Dead PC"

We start by making the PC as small as possible. We don't need drives, or more than one stick of ram and so on. If that doesn't show a display we continue to make it smaller and smaller until we are left with as few parts needed to get a power up and beeps since the display is not working.

-> How do you know the display is good? Be sure to test the disply on another source before you work on the PC.

Example: An owner was upset their PC would not display. I had to show them how to get the display to use the right input from the PC (the source button on their monitor.)