In the end, I managed to find the password in an old browser config in my previous OS installation.
Seriously - how can Crytek/EA possibly think that ignoring thousands of paying customers who simply want access to their game is justified? This is the worst kind of rank-amateur disregard for customers and customer service which makes the game industry look so damned unprofessional.
Still, I guess they've got everyone's money. They don't really give a damn what happens after that.