It doesn't necessarily have to be your social security. It could be some random number given by ADA. Check your e-mail that ADA sent you once you applied to sign up for DAT.
Here is the procedure:
1. Go to ADA.Org and apply to take the DAT.
2. ADA approves it and send you an e-mail with your eligibility number. Approval cycle runs every Tuesday so if applied on Wednesday then wait until next Tuesday to receive an e-mail from ADA.
The e-mail will come from the sender "education" and the subject "DAT eligibility letter and checklist."
3. Once e-mail with the eligibility ID is received, it advise you to wait for 24 hours and then go to Prometric.com or call them to schedule your exam.
Your DENTPIN is your eligibility ID. If you still having trouble, call the Department of Testing Services (the number is in your e-mail, I am not sure if I can post the number on this website).
This is my understanding of the procedure, please correct me if I am wrong. If you still having trouble, PM me and I may be able to provide you with their phone number. I hope it helps.