Stuck in a F'fox 9 Sync configuration loop - account already exists but can't manage account-

Question

I'm stuck in a loop trying to configure and use Firefox 9's Sync feature.
On System "A", I have used the Set Up Sync tool to create a Sync account: I belive the account is valid insofar as I can use the email address and password supplied to the Set Up Sync tool to log in to the Web-base Sync portal.
But if I then use Tools —> Options —> Sync to manage my Sync Account or Add a device, all I see is a Set Up Sync button; no Manage Account button or features. AND if I try to re-create my Sync account, the tools reports that the email address is already in use.
On system B, the behavior is essentially identical. I can't CREATE a Sync account with the same email address as System A, but I also can't manage or add devices.
I've been using computers since 1981, and generally can work through these issues. But I'm completely confounded: It seems I've successfully created a Sync account, but on two computers Firefox 9 refuses to permit me to manage or otherwise use that account.

Answer 1

Thanks for the solution. It was *definitely* helpful.
I must say that having worked through the configuration, I did NOT experience the usual "doh!" or even an "ah ha!" moment ala "Oh, I was so thick not to figure this out".
That is to say that, thanks to you, I now have a better understanding of how to make Firefox Sync work, but the steps and controls still seem a bit convoluted and opaque to me.
That notwithstanding, thanks again for your help.