Chris the first thing I would do is remove the bobbin plate and needle plate, which means you will have to remove the needle if it is stuck in the hook/race area! Cut all the thread out you can and get a flashlight and look for a thread caught in there somewhere! I had the same issue with a FW - it had a long hair wound around and around the hook/race. Everything was frozen up solid until I oiled and oiled and finally got that hair - along with some thread out! Look from the top and look from the bottom. You are sure the needle was in correctly and tightened? If the culprit is not a thread jam, you may have a timing issue - but, those 66's were such great machines I don't see the timing as a problem. I bet it is a thread caught in or around the race that you haven't seen yet!
Nancy