Unearth,
You said that your PC is an older HP Pavilion. Please reply with the MODEL of your HP Pavilion.
You can go directly to:
http://www.hp.com/#Support
Put in your model Number (i.e. Pavilion 9100) and go to the specific support site for your HP model.
Based your recent posts, as other here, I'm inclined to think there is some type of hardware failure with your PC - i.e. motherboard or power supply.
However, if the PC went from randomly shutting off to completely NOT working, it's possible that when you opened it up and cleaned it, you inadvertently disconnected some connector/cable or jarred a card or component loose from the motherboard. If THAT were the case, re-connecting all of the connectors should get it back to the state it was it.
If you attempted to replace the power supply - what power supply did you replace it with and how did you reconnect the new power supply - this too could be the source of your problem if the power supply wasn't correctly replaced.
What I'm saying is that there are MANY possible causes to this problem based on your specific hardware and what has been changed or replaced since it was "kinda" working to the point where it is no longer even powering on.
Please reply with more info and myself or someone else here should be able to assist.
- John