Then you may be looking in the wrong folder. The TS3W.exe will be in one of the following locations:
Program Files/Electronic Arts/The Sims 3/Game/Bin
Program Files(x86)/Electronic Arts/The Sims 3/Game/Bin
Program Files/Origin Games/The Sims 3/Game/Bin
No, not DOCUMENTS wrong folder. Go to the boot drive first (usually the C drive.
You can reinstall just the base game and have the EPs stay installed and working so I would try that first. Okay? You don't have to lose your stuff. Follow my directions. I have had people do this many times.
Move the The Sims 3 folder from (My) Documents\Electronic Arts\ to the Desktop.
Uninstall base game
Install base game
Patch the game
Run the game make sure it works
Delete The Sims 3 folder in (My) Documents\Electronic Arts\
Move The Sims Folder from your desktop to (My) Documents\Electronic Arts\
Yes, you can reinstall the base game and the expansions packs will stay installed and working.