Hi Dagher,
I just checked this on my test environment, I have Excel 2013 (15.0.4420.1017) MSO (15.0.4420.1017) 32-bit, when logged on with Users account, I could still open the PowerPivot, I checked serveral feature, also worked.
Suggestions:
1st, try check for the latest update for your Office, and install them if you haven't.
2nd, since the Users account might not have enough permission to access network resources, check if there are any external data in your workbook.
If you can still use a workbook with local data source to reproduce this behavior, please provide the detail steps so we can check on it.