Put simply, the goal here is to clean install Windows 7 on a virgin, unused PC. You can boot and run Setup with the Upgrade media for Windows 7, but when you go to activate, it won't work.
After performing the clean install, ensure that there are no Windows Updates pending that would require a system reboot. (You'll see an orange shield icon next to Shutdown in the Start Menu if this is the case).
Then, open regedit.exe with Start Menu Search and navigate to:
HKLM/Software/Microsoft/Windows/CurrentVersion/Setup/OOBE/
Change MediaBootInstall from "1" to "0".
Open the Start Menu again and type cmd to display a shortcut to the Command Line utility. Right-click this shortcut and choose "Run as administrator." Handle the UAC prompt.
In the command line window, type: slmgr /rearm
Then tap ENTER, close the command line window and reboot. When Windows 7 reboots, run the Activate Windows utility, type in your product key and activate windows.