|Hard to relate your "no signal" symptoms to Windows Update - assuming you never see anything but this on the screen. As said above, eliminating the monitor from the equation is the first thing to do. When you get "no signal" it can be down to quite a number of possibilities.|
If it is not booting up (and I accept that is not easy to prove) then it is unlikely to be the display module or card. We are not in the position to be certain but from what you have said it is not booting normally, so PSU is quite likely.
Better clarify that Display card and Video card are alternative names for the same thing. Most HP's usually come with an inbuilt module rather than an addon card - although a card can be added instead of using the module.
Sorry but without having "hands on" we can only generalize and mention items which have been known to fail fairly often. You might have to resort to taking it for repair.
Always pop back and let us know the outcome - thanks