Don't immediately jump to the conclusion that it's a bad motherboard. It's probably a component, but which one is up for grabs.
I've had this kind of problem with a bad power supply. Replacing the power supply ultimately took care of it without much difficulty (and fortunately, they're not too expensive). Other things could be a bad CPU fan, bad vid card fan, bad memory, bad mobo... basically, any component.
What I'd do is take it back to the computer shop you were just at, explain what happened, and ask them to turn it on and run it for an hour *with the covers on*. That's important, because when they're working with it, they likely have the case open, and heat dissipates quite nicely. Once they see the problem in action, they should then be able to diagnose and repair.
And in the meantime, see if you can find a machine to go gaming on. Times like this, it's good to kill something...
