yup... if you suspect the UPS just plug straight to the wall. If nothing happens than it's likely the power supply.
Hope you get it running soon.
And yes..... you do need to clean the dust out of the vents and cooling fins once in a while. I work with some computers that do a specialty job.... running a life safety security system. If the vents get clogged, and the CPU fins too.... the computer server will crash and blue screen due to the heat build up.
Keep those vents and fins clean. Those fans suck in the dust.