Here's a link to your laptop's parts. Toshiba often doesn't make their laptop mobos available to anyone but themselves, and unfortunately that seems to be the case here.
That said, Toshibas are very difficult to service. Instructions are often not available for how to do anything beyond replacing ram or a hd. Your model fo laptop is running around $400-450 used so it's not worth it to fix it. I'd just part it all out on ebay, you should be able to earn a couple hundred bucks and put it towards a new laptop.