I had this once and took it to the repair shop. Mine was like yours - I could see the bit underneath moving, but the case wasn't. It would move a little and stick - wouldn't pick up the thread at all. Turns out, when I replaced the case, although I was putting it in correctly, the hand wheel was in the 'wrong' position.
All it needed was to be moved a half turn or so and the bobbin case re-inserted
The same thing happened again recently, but this time I was able to fix it by just moving the wheel until the bobbin moved correctly.
Good luck!