Gateway Laptop Motherboard problem or just fan?

I have a Gateway Laptop, M-6816 dual core. I've only had it 14 months and the computer will shut down on you when you're right in the middle of something. It sometimes has a hard time booting up when you first turn it on. I took it to Best Buy where I bought it (of course the warranty has expired)! They think it might be the mother board, but the fan isn't working either and the computer gets really hot. So do you think it would be worth ordering a new fan for it and see if that takes care of the problem, or do you think it probably has motherboard damage? It gets pretty hot only after about 5 minutes of being on the computer. The computer will work for us sometimes, you can go on line, the files are all there still... so I'm thinking it could just be the fan. I paid about $750 for this computer. Any suggestions?

I was shown where the fan is but I'm a little nervous to take it apart. Gateway needs the serial number off of it so I guess I'm going to have to take it out. I was thinking once I ordered the new fan, maybe bring it to someone that knows computers pretty well and have them put it back in for me... maybe it's not that hard at all. I heard the fan costs about $79 to $100, I sure that is the problem. How can you tell if the motherboard is damaged?