@Phaewalker Please repair the game through Steam. The option is called "verify integrity of the game files," and it's somewhere under Properties, perhaps under Local Files. (It's moved around at times.) Then try to launch the game through its executable, TS3W.exe (with the W), or a desktop shortcut. The .exe is inside your Steam game library, here by default:
C:\Program Files (x86)\Steam\steamapps\common\The Sims 3\Game\Bin
You shouldn't need to have Steam or the EA App open in order to play, at least not after the first time you launch the game.