Oh sugar, now I've really bust it

mech_2

The lack of beeps from the motherboard might just be because there's no internal speaker. I can't see any signs of a connection to one in the photo.

I doubt the processor has burnt out. As long as the heatsink is on it at all it's probably fine. They're more resilient than the motherboard in my experience.

It's possible the motherboard was zapped with static electricity when you were cleaning out the dust. That doesn't necessarily mean it's dead either. It could just have had all its settings scrambled. I've known that happen.

The easy way to reset it back to factory defaults is to take out the battery for the memory that holds the settings. Just for a few seconds and then replace it. It's the thing the size of a penny which looks like a watch-battery in the middle at the bottom of the photo, behind two black cables.

It's a last ditch suggestion, as it might also reset other things you don't want to reset and may not know how to reconfigure. But I would try it before throwing the PC away or taking it to a shop for repair. If that was indeed the problem it should at least get something to appear on the screen. And if it gets that far there's a good chance it will also boot into a usable state without any further reconfiguration.

Just a thought.