The uninstallation option in the Windows Control Panel is usually more than sufficient. Your description suggests there are other problems with your Windows installation and you should try to fix that before going any further. Depending on the nature of the problem this may even mean reinstalling Windows (and all your apps) from scratch.
As for obtaining another copy of Office 2010, all you need is your product key and a visit to:
http://products.office.com/en-us/buy...oduct-key-card
Your Office 2010 product key can be retrieved by using magical jelly bean keyfinder:
https://www.magicaljellybean.com/keyfinder/
FWIW, many Office users regard the Office 2013/365 interface a backward step and, unless you need to use the new features introduced with Office 2013/365 (which also means you can't share those documents with users of Office 2010 & earlier), you might be better off sticking with Office 2010.