I've tried the "forget your password" link but it's useless. It sends me a link via email, and the link sends me back to the same exact screen, where I have to enter my email to be sent a reset link. It's like a viscious circle.
No answer from support either. What exactly can I do?
Yes, this is a current glitch, affecting a few advertisers. Work is in progress to fix it, as you may well imagine.
I'd suggest calling or writing AdWords support (adwords-support@google.com). Please include some information that helps to verify that you belong to the account (this is for your protection, of course). For example, only the account owner would know the exact amounts and dates of recent charges - which you can get from your credit card statements.
With verification, we can then create a new password for you, to get you into the account. You'd want to create your own unique password from within the account ASAP, of course.
Again, sorry for the trouble!
AWA