You can try to check the Event Viewer to see if there's anything that stands out just before your computer randomly restarts.
Don't totally assume that it's the motherboard (or any one specific thing). It really could be a handful of possibilities. Easiest thing you can try is to remove a stick of RAM and see if it still happens. If it does, put the RAM back and take out a different stick, etc. Bad RAM can cause strange shit to happen.
Theoretically, you could test to see if it's your hard drive by creating a bootable standalone image of Windows on a flash drive. I use it a decent amount at my job and it's pretty awesome. I can help you with this if you wanna add me on Steam.