@studio__savannah Have you previously been able to login at the launcher and/or Main Menu? If so, the problem is not likely to be due to your disc install, or we'd have a lot more reports of problems, and plenty of people still use discs. (Of course, if you'd never registered your discs with Origin at all, your account wouldn't have TS3 on it, so I wouldn't expect you could login.)
I take it from your post that clearing Explorer's cache and removing your game folder from Documents didn't work. (Did you repeat these steps together? Just checking.) The other thing you can do is clear all of your browser caches together, login to some other EA site like ea.com, change your password, remove your entire TS3 game folder from Documents again (it's fine to delete the new one if it doesn't have any content), and then try to login to the launcher or Main Menu again.
If this doesn't work either, please let me know, and I'll ask an EA community manager to look into this. There are occasional login issues, but they usually get cleared up quickly.