Windows Update Hangs on "Checking For Updates"

I'm hoping y'all can help me with this issue with my friend's system, running 64 bit Home Premium, Avast, and Java, Flash etc. all updated. It's stuck at "Checking For Updates."
Yesterday I installed an update to the Windows Update Client, KB3138612, and the System Update Readiness Tool. After that, 62 updates were ready for download, and I successfully installed them. After restarting, a window came up to upgrade the browser from IE 10 to IE 11. I did so, then ran Windows Updates again to check for security updates to IE 11. Stuck in an endless loop again.
I reset the Windows Components with FIXIT 971058. This resolved two errors: Reset Windows Update Data Store (Root Cause) and Service Registration Missing or Corrupt. Still stuck in a loop.
I installed the latest version of the Windows Update Agent and rebooted. Still no joy. Any suggestions would be greatly appreciated. I looked over the contents of the CBS.log before coming to this forum. Something is definitely wrong, but I can't make heads or tails of it.
Here's the link: https://1drv.ms/t/s!AiuNs_2Ik1SigQsc8snLSRVeKcNM

Windows Update was stuck on Searching For Updates, I found this information after nothing else helped and this worked for me on Windows 7.

Method 1:
1. Click Start
2. Type ‘cmd’ in the search bar.
3. Right click Command prompt and choose “Run as Administrator”
4. At the command prompt, type the following, commands and then press ENTER after each command:
a. net stop wuauserv
b. net stop bits
c. net stop cryptsvc

Please do not close the Command Prompt window.
Method 2:

Rename folders pertaining to Windows Update.
At the command prompt, type the following commands, and then press Enter after each command:
a) ren %systemroot%\System32\Catroot2 Catroot2.old

b) ren %systemroot%\SoftwareDistribution SoftwareDistribution.old

At the command prompt, type the following, commands and then press ENTER after each command:
a) net start wuauserv
b) net start bits
c) net start cryptsvc

Close the Command Prompt window and check the issue if issue reoccurs

Hi T,

Can you run this tool, copy/paste the output.

http://go.microsoft.com/fwlink/?LinkID=52012

Roy