Been told my problem sounds like the

been told my problem sounds like the motherboard,had been using pc (dell dimension 9200) for 15min other day when it died,couple of times when i switched it on it got as far as the dell logo but no further and last time didn't even make it that far,it also powers up by being plugged into mains don't even need to touch pc power button.don't know if it's connected but for past few months when i've shut it down occasionally it wouldn't, could leave it all night and next morning it was still shutting down