MissJag93 Skip the online login for now. The login at the launcher doesn't do anything at all; the one at the Main Menu is only for the few online features like SimPort and badges. The rest of the game plays the same whether you've signed in or not.
To clear the "connecting" status, open Keychain Access, inside Applications > Utilities, search for sims3 , and delete any entries you find.
If you do want to try to login at some point in the future, do so at the Main Menu, not the launcher. And make sure your password doesn't contain any special characters, only letters and numbers. While special characters work fine on other EA sites, Sims 3 doesn't handle them well.