Contacted support by phone and they confirmed they are aware of "some server issues" that may be causing support ticket and product registration trouble. Said if you need products registered or support tickets created you could call them by phone and they can do either for you.
Edit: It sounds like people are still having issues with this, but I'm going to accept this as the answer for now since calling them directly appears to be the only way to register a product or create tickets. (Come on, PreSonus, get your support site together!)