I had the same problem but eventually found a clicky box which enabled me to register my car on their system, sorry can't remember exactly how.
In saying this I made 2 crossings in April and I can't get them to take the payment from my account. They say their systems show my car as disabled and free from charge. I paid a full years tax when I bought the car at the beginning of December and DVLA have confirmed in writing my car is no longer shown as disabled on their system. Dart Charge systems must be well out of date.
At least I have plenty of emails to prove I tried to pay.
Try
[email protected] if you can't get through on the phone.