Better Business Bureau has no legal enforcement authority. All they do is log your complaint internally and increment the number of complaint statistics by one.
If you go legal route, more than likely, you'll have to sue in the city Mouser is in. Most companies stipulate that in their policy. By buying an item from that company, you implicitly agreed to it.
I really sympathize with your predicament though. Just send them a detailed description of your problem once, and if no reply, go to ST directly. That's probably the fastest and easiest route. Sueing a company for $300 product is just silly. It'll cost you more than just buying another one.