This article contains information about how to modify the registry. Microsoft cannot guarantee that these problems can be solved. These problems might require that you reinstall the operating system. WARNING: Serious problems might occur if you modify the registry incorrectly by using Registry Editor or by using another To determine your user account type in Windows for help. If you’re not sure if you’re logged on with an administrator account, refer to How If your computer is part of a network, you might have to ask the system administrator for help. Note: You’ll need to be logged in with an administrator account for this method.
If none of the methods above worked to uninstall Office 2010, try removing Microsoft Office 2010 manually. Note that if you had a traditional installation of Office 2013 (not 2010) you'll be looking for 'Office15' references instead of Office14: OK, looks like there is some remnant of the old Office somewhere.