You are using a version of Office that uses "click-to-run" technology.
Versions that MAY use this are:
+ Office 2010 Starter
+ Office 2010 Home & Student
+ Office 2010 Home & Business
There are FULL downloads available as well for each of these products!
If you want to eliminate the Q: drive (and all its issues) you may:
+ Uninstall (from Control Panel) the "click-to-run" version already installed
+ Download and reinstall the FULL (MSI based) product of the version desired
Procedure to get FULL version:
+ Visit the site where you purchased Office 2010, and sign in by using your Live ID.
+ Click My Account at the top of the home page to access your Office 2010 downloads.
+ Click Download for the suite you purchased, and then click Advanced Options under Download Now.
+ Download and install the version of Office 2010 listed that is NOT an Office Click-to-Run product and that does NOT require the Q: drive.
The product key validation, unfortunately, is part of the media for each product. However the key you are using will work for BOTH "click-to-run" and "MSI" type installs of (in your case) Office Home & Business.