To use your on board you probably have to go into the BIOS and enable it again, even with your current card installed you should get SOME kind of a picture, maybe not a great one but a minimal one. So therefore, (I think) that your on board is disabled in your BIOS. Not a guarantee, but I know on board audio works the same way. Probably being as it was a custom build, Best Buy disabled that in an attempt to force you to come back to have it serviced.
As far as your heat issue, I would say too, use the canned air, make SURE your fan is spinning, and make sure your heatsink is attached. those are two BIIIIG things. I actually was having GPU issues too, because my fan locked up and melted the plastic at the end of the fins on the heat sink, in turn, torching my GPU. It sounds to me like your fan may not be spinning. Another possibility (I have seen this believe it or not) is that your thermal paste almost solidified and isn't doing much. Before I buy a new card, I would try cleaning the processor off and replacing the thermal paste. It is a $10 investment rather than a $100ish investment. Good luck and let me know if this helps.
