I'm having the same issue. I've been thinking about getting BF4 and saw that it was in the 'Origin Game Time' section on the Origin shop so I thought I'd give it a try first; make sure I'd get enough use out of it.
It says I've used all my game time already - apparently in the 8 hours it took to download I've used 7 days worth of game time and tries to force me to use an activation code.
So I guess I won't be buying BF4. If EA can't be arsed to get their game time functioning properly then I'm not going to trust them to keep the game itself running properly.