I had trouble logging in and linking my origin account with Sim3.com as well. Clearing cache and using different browsers didn't work for me, but what I did truly worked for me was changing my origin ID and using a different email (I used firefox).
I went to my Origin account first and changed the information (ID and Email) then logged out of Origin and uninstall Origin. Then reinstall Origin and use the changed email and password into Sim3.com login page. Click the persona which is the new ID and click the options boxes and signed up. It should worked successfully. Once you are login it will say your partial log in and needs the game key. The game key can be found in Origin (if purchased from Origin) by clicking the sims game in "My game library" and right click for the option "Game properties". You may not have to look for gamekey, if the Sims3 automatically logs you in because it connects to Origin. But it asks for it, do as instructed to find game key or Google how to find game key in Origin. I hope this help!
BTW I'm just a regular person who was dealing with the log in issues for couple of weeks (major headaches). Not a EA worker/Tech or anything like that lol. Please tell me if this works for you.
