Same exact problem, so suddenly. But also with offline payment method (type cod). It's really weird, I can't find the cause, let's hope someone can figure out the problem.
UPDATE: in the log I found thi s error: "Frontcontroller::init - Cart cannot be loaded or an order has already been placed using this cart"
Do you have it too?
UPDATE 2: it seems that the problem can be attributed to order states. I'm investigating ...