Well technically that could be the case. There are more than a handful of other problems. It's hard to understand what happened but since you say that the computer will actually boot to windows or what ever OS you are using. It sounds like it is just overheating. I would do the following:
Unplug all connections
Open the case
Remove CPU fan/heatsink
If there is THERMAL PASTE on the CPU, I would then remove it with alcohol swabs, and buy some new thermal paste and apply it.
(Before you apply the thermal paste, take the cpu out of the socket and make sure there arn't any bent pins on the mobo.)
If there are bent pins you need a new mobo.
If there is NO THERMAL PASTE, that means that it obviously is just an over heating issue, and you need to buy thermal paste.
If this does nothing, I'm sorry its probably a bad motherboard.
You could probably find a replacement for a LGA 1156 board somewhere on the internet or at your local computer shop. Keep in mind that when you go to a computer shop, the board should only be around $50-80 for a medium end board. Therefore it would be better if you purchased one of newegg.com or some other website.
The only probably with replacing the board is that you will have to completely uninstall Windows or your OS, install a new one, and then install all the drivers for the new board. This is quite a hassle and I wouldn't bother doing it.
You could get an i5-2500k/i7-2600k and a mobo that will work for around $300-500. It probably sounds like a lot but it is worth it. Then you just need to redo the operating system, buy the ram and such. (Practically I'm telling you to build a new computer.)
If you need my help on pricing and parts for the computer, I'd be happy to work with you in finding parts on newegg.com. Just tell me your price range. Thank you. Sorry if the board doesn't work.