Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hi,
In order to uninstall Office 365 installation files from the Computer, you may run the fixit available in the link below which removes the Office traces automatically.
http://support.microsoft.com/kb/2739501
Also run the fixit available in the link below which would remove the Office 2010 traces from the Computer.
Once done you may try to re-install Office 2013 and check if you’re able to work in this Office version.
Regarding your query of service pack 2 for Office 2010, are you unable to download?
Provide us the detailed information about this problem to assist you further.
Thank you.