The game does require activation through Origin to work, so I'm pretty sure that you have connected it to an account at some point.
In the interest of full disclosure, here is where your key is stored:
You can access the Registry Editor by holding down the Windows key + R and typing "regedit" (without quotes) into the Run prompt.
1. Expand the HKEY_LOCAL_MACHINE folder by clicking the triangle next to the folder icon.
2. Expand the SOFTWARE folder.
- For 64-bit systems, expand Wow6432Node
3. Expand the Maxis folder.
4. Expand the The Sims folder.
Your key should be the Product GUID line. 🙂
Hope that helps!
