You find the procedure at:
http://www.sevenforums.com/tutorials/42776-extract-files-windows-7-installation-dvd.html
Extract and replace the %SystemRoot%\System32\DriverStore\FileRepository with the following folders:
atiilhag.inf_amd64_*
atiriol6.inf_amd64_*
nv_lh.inf_amd64_*
Extract and replace the %SystemRoot%\winsxs with the following folders (x64):
amd64_atiilhag.inf.resources_*
amd64_atiilhag.inf_*
amd64_atiriol6.inf_*
amd64_nv_lh.inf.resources_*
amd64_nv_lh.inf_*
Extract and replace %SystemRoot%\winsxs\Manifests with the following files:
amd64_atiilhag.inf-languagepack_*.manifest
amd64_atiilhag.inf.resources_*.manifest
amd64_atiilhag.inf_*.manifest
amd64_atiriol6.inf_*.manifest
amd64_nv_lh.inf-languagepack_*.manifest
amd64_nv_lh.inf.resources_*.manifest
amd64_nv_lh.inf_*.manifest
Note: these are the 64-bit version of the files. For the 32-bit version look for the x86 files. You also need to replace the permisions on above mentioned files and folders to be able to replace them. A procedure to accomplish this is here:
Fix “You need permission to perform this action” error
After replacing the folders and files, reboot your computer. Then start the cmd-prompt as administrator and do a sfc /scannow to verify that everything copied correctly and verifies 100%.
{SNIP}
After applying the System Update Readiness Tool, the SP1 installed successfully. Seems the tool (Windows6.1-KB947821-v10-x64.msu) did the trick. I downloaded the SP1 (windows6.1-KB976932-X64.exe) and ran it. This time the SP1 installed itself and ran without any problems whatsoever.
My suggestions to fix the error Code 800F0A13 is the following:
Extract and replace the above mentioned files and folders. Reboot. Download and run the System Update Readiness Tool to fix any remnant errors and do another reboot. Then either download the SP1 and apply it manually or try the Windows Update.