This is the history of my attempts to get around the problem.
I just tried to install Windows 8.1 GA from Windows 8 Home.
Downloaded 8.1 Pro from MS Store OK.
Error message at end of installation. Error Code 0x80004005.
Tried again, several times with the same result.
Searching through Microsoft Community I found this thread.
I disconnected all the external devices (printers, scanner, USB (universal serial bus) drives, etc) except mouse and the keyboard. - No change.
I disabled the antivirus/firewall software. - No change.
I placed the computer in a clean boot and then tried to install the upgrade. - No change.
The only worry is that the download had already taken place and I was installing from the existing download.
I next deleted all the temporary files and restarted the download from scratch. Again I got Error Code 0x80004005 at the end of the install.
I'm running out of ideas.