Hi,
Regarding of this issue, I have a couple of questions:
1) Was Office 2010 pro plus deactivated after installed Windows 10?
2) According to your description,>>Where is the Activation key now the computer has changed companies and locations?<< Did you migrate this pc that installed Office Professional Plus 2010 to a new company and location?
As far as I know, Office Professional Plus 2010 is usually using Volume License. I recommend you connect the Microsoft Volume License service center to get more help.
https://www.microsoft.com/licensing/servicecenter/Help/Contact.aspx (PS: Select your country or region to see the phone number for your area)
Hope it's helpful.
Regards,
George ZhaoTechNet Community Support