My issue was finally solved.
6 days after opening the ticket I got this message from support:
I am very sorry for the delay, please log in to your Poloniex account and fill your profile level 1 information at:
https://poloniex.com/profilePlease use the same information you have previously used.
Let me know when you are finished and I will send it for verification immediately.
I did as told and my account was re-enabled quickly.
Withdrawing my BTC also worked well.