Burnt dust isn't really dangerous, although it does smell a bit unsettling. It doesn't get hot enough for it to catch fire, just give off the distinct smell. It is most likely coming from the power supply, if you have a desktop PC.

If it isn't dust, it could be a blown capacitor, but you would probably hear that as a pop in your PC, and the smell from that wouldn't stick around for a long time. It's not nearly as likely to be the case as just dust, though.

Do all the fans spin when it's on? If one doesn't, a lot of heat could build up on that component and the dust on it. If a fan is stuck, it could either be because of too much dust buildup, or it could be a broken ball-bearing. You probably can't fix the latter without replacing the fan entirely.

Are you guys serious about never having seen cans of compressed air? <,<