Got the following response from Google to my note about
signup bug:
Technical issues are currently preventing our partners from signing up for a Google Book Search account with their existing Google logins. Our specialists are working hard to resolve this issue, and we apologize for the inconvenience.
If you would prefer not to wait until this issue is resolved, I encourage you to submit a Google Book Search application with a different email address.
So I followed the advice and tried to sign up with a new email address. The result:
At the moment, it appears impossible to sign up for the Google Books Partner Program. I've followed up with Google.