Dell Inspiron 20 All in One will not boot

I have a Dell Inspiron 20 all in one desktop. I left it running last night to finish up some file conversions. When I got up, it had shut down and now will not boot. I press the power button and the lights start but then it shuts right down again. I've even tried unplugging the power cord for a few minutes and plugging it back in, still no go. Of course the warranty is expired. Anyone know of a solution?