Just to be safe, if you're using a compressor don't blast it with too much pressure or you can end up with issues, be careful with that.
A PC could overheat in a few seconds without adequate cooling, so if there's quite a bit of dirt in that fan, it may overheat that quickly.
But, you said you can use the mouse, if you click it freezes, makes me think that it is still an OS related issue.
When it beeps, what sort of beep? A long beep or a few beeps for example?