|It's probably not the monitor. The blue screen is probably just what it shows when it's connected but not getting a signal but I guess it wouldn't hurt to try another one if you have one.|
Another thing you can try is to disconnect the power cord and open the case and temporarily remove all the cards (except video if you're using a video card) and disconnect all the drives. Then reconnect the power cord and see if it powers up to a posting or logo screen. If so then one of the disconnected devices must be at fault. While you've got the case open you can check and make sure all the connections are tight and there are no frayed wires.
If it still doesn't come up then you're left with the power supply or motherboard or both--both because sometimes when a power supply fails it wrecks the motherboard as well. Many of those HP/Compaq systems used low quality power supplies so it's a good guess that that's the problem. If you have a known-good compatible power supply you could try swapping it in and seeing it it works then.
There's also something often called a 'power supply paperclip test' to test a power supply that's been removed from the system. I believe it's a no-load test so that even if it passes a power supply may still not work in the system. Here's a pdf download that describes that if you think you might want to try it: