If you are not receiving the emails sent from our login system and you also are not seeing any autoresponse email from opening your ticket we should assume that emails from our system are not reaching you.

Please use an alternate email account to email contact@digitalocean.com. Our team can check the most recent email attempts and if our system has imposed a block on outgoing emails (this can happen if emails are bouncing) our team can remove the lock.

please tell us if you use email account from microsoft (like @outlook, @live or @hotmail, @msn)
if yes, than the issue is that microsoft mailservers dont like any other mailserver except themsself.

So look in the spam folder, if you have luck than the mails will be there stored.