Ok, I brought it a shrubbery and it let me in.

Actually, I did just get in and downloading now, so may just be a delay/database update/timing kinda thing.

In between though, I'd also:
-opened the registration confirmation email from them
-logged off/
-rebooted/logged in again so had a new IP. Who knows.

Anyway, to save anyone else some frustration, I did notice that while stuck in the loop, even after repeatedly "logging in" the indicator at the top of their page never did actually change from the "Login" indicator to "Log Out" as displayed now and circled in the capture above.

That is just to say that I assume you should quit playing its game and bail if it still says LOGIN after filling in the login boxes - it will change when it actually lets you in.