it is very upsetting to have that happen. I am going to tell you some stuff that you may not want to hear, but you should hear so that you can best understand your legal standing.
You have to understand that there is a difference between what we WANT and what we are legally entitled to.
You said, "I have just read the warranty and it does not mention anything about motherboards". They DO mention that warranty is for a defect in materials and workmanship" And they DO exclude accidental damage.
If the damage was as you described, it was most likely caused by someone tripping over the power cord. This is a COMMON issue. It is also common to have this for people who trip over HDMI cords. This is accidental damage, not a defect in workmanship or materials. This is not just a Toshiba thing. I have worked for all three of the big 3 computer OEMs. Kasey is being a bit disingenuous. There is NO such title as PC guru. If he was an A+ certified tech, he wouldn't tell you to try consumer protection. if he was a certified system builder, he wouldn't tell you that either. If he worked as an IT tech in the industry he would tell you our most common repairs are for dropped units or units with the cords kicked out. If he worked for an OEM, he would have told you the same info I told you.
If they were an apple "genius" Kasey would have told you the same thing I told you. Apple had/has the same issue with their machines too. That is why they are experimenting with magnetic connectors. They break away without damaging mobos. The trouble is they short out because of staples that are on desks.
You have NO legal standing based on a US warranty. You have NO standing based on "consumer protection". Your BEST bet is not to try it on a legal basis, it is to try to do it on a CUSTOMER COURTESY basis. Do what we call an "executive carpet bomb". You should go on the internet and look up the email addresses of every executive for the company and email them a letter appealing to them. they have large budgets at their discretion. If you have a good letter and you "win them over", they can tell their subordinate to fix your computer for free or they can tell them to give you a new one. DO NOT threaten any legal action. If you do, they will NOT help you. Again, you have NO legal basis for any lawsuit.