Update: I tried to contact support to see what was the best way to send them the documents they needed for unblocking my account. This was their response:

Thank you for your interest in Coinbase. Our primary goal is to make our platform safe and secure for our customers. Coinbase is a regulated Money Services Business under FinCEN (FinCEN.gov), and as part of our responsibility, we are legally obligated to implement regulatory compliance mechanisms.

We regret to inform you that we are no longer able to support your Coinbase account as well as any other accounts you may have created. Please note, we have not blocked access to the balance currently in your Coinbase account; while we can no longer process brokerage orders via our banking relationship, you may still send your balance offsite to an external address.

Please be careful when dealing with this company, and remember that even if you're in the US there are many alternatives (LocalBitcoins, Circle and Gemini come to mind).