I've had this very same issue for a long time. It wasn't until today that I humored the possibility that my web browser was not compatible with the T-Mobile website. I almost exclusively rely on Google Chrome, but at the suggestion of one of the members of T-Mobile's support team, I changed my browser to Internet Explorer, and it worked perfectly.
With Chrome, I could access almost any page EXCEPT for the Account page which is the one I'd need to change my plan. With Internet Explorer, I can get to the Account page AND all of the links on it work, too. Give IE a try.