@vt102a According to the minimum requirements, you should technically be able to run the EA App since you're also running a 64-bit version of Windows 7 SP1. However, I'm not surprised that it didn't work when you installed it.
I'd like to see any relevant errors from the App as well. Hit Windows key-R, enter "perfmon /rel" without quotes, and you'll see a chart of errors and updates with a column for each day. Please look for the most recent error that mentions the EA App (or EA Desktop, or something like that), right-click on the error and select "view technical details," copy the info you see, and paste it into a reply.
Out of curiosity, when you've opened Origin offline, can you launch Sims 3 from TS3.exe? If you don't have a desktop shortcut, you can find the .exe within the game's program files, likely here if you installed through Origin:
Program Files (x86)\Origin Games\The Sims 3\Game\Bin