From your description, it sounds like something has definitely locked up. What I generally do is to pull the pump and motor off, then try turning the transmisison lug manually. Things that can cause the coupling to burn could include something stuck between the inner and outer tubs. This you can check by removing the outer cabinet and the tub cover.
It is not uncommon for the gearcase to lock up, so if you cannot turn the drive lug, a new transmission is in order. I would also replace the clutch/brake assembly at the same time to restore the washer to like-new condition mechanically. Replacing the entire assembly is fairly straightforward, and the videos can be found somewhere on this website to guide you along.