When attempting to activate Microsoft Office 2010 receive error
"An unspecified error has occurred. Your request cannot be processed at this time.
Please try again later. (0x80070190)"

This is another instance of UAC interfering where it does not make sense.

Enter the key as you would normally do so.
Then you have two options Simple and Complicated , both work

Option 1 Simple

After update , Simply start any Microsoft Office 2010 application , Word , Excel etc.
with Administrator privelges & then activate.

You only need to do this once to activate   

Option 2: Complicated

Open a command prompt with Administrative privelege.
Navigate to one of the following folders.

Win 7 32 bit
C:\Program Files\Microsoft Office\Office14

Win 7 64 bit with 32 bit Office
C:\Program Files (x86)\Microsoft Office\Office14

Run the following command
C:>cscript ospp.vbs /act

You should see something similar to the following.

C:\Program Files (x86)\Microsoft Office\Office14>cscript ospp.vbs /act
Microsoft (R) Windows Script Host Version 5.8
Copyright (C) Microsoft Corporation. All rights reserved.

Installed product key detected - attempting to activate the following product:
SKU ID: fdf3ecb9-b56f-43b2-a9b8-1b48b6bae1a7
LICENSE NAME: Office 14, OfficeProPlus-MAK edition
Last 5 characters of installed product key: XXXXX
<Product activation successful>

DONE. Thanks to PaulNSW

If it helped would appreciate a rating star.

Microsoft Certified Partner