Clean it first.  - Then make sure all your fans are spinning. 
Heat causes all kinds of wacky problems with electronics. 
If after a good cleaning she keeps shutting down, then you can figure out what's causing your problem. 
At least then, if it is the power supply, or motherboard,  you wont get a face full of dust replacing them.
My old box was so dirty that when the power supply intake fan died, i couldn't tell from looking at it.