Windows 7 could not search for new updates Error code C80003FA

C80003FA ReadVerifyFailure  - A read verification error occurred.

1. What is the installed antivirus/security suite ?
2. Is a 3rd party firewall installed ?
3. Is this an upgrade from another Windows edition ?

Please click the Start orb. In the Search programs and files field type in wups2.dll

Under Programs right click wups2.dll and choose Properties, click the Details tab when the Properties window opens.
Both the File and Product version should be showing 7.4.7600.226
Now do the same for wuaueng.dll
It, too, should show File and Product version as 7.4.7600.226
 
If the File version is earlier than that, you'll need to install the most recent Version of the Windows Update Agent.
The simplest method for doing so is to download and save the Fixit found here - How do I reset Windows Update components?
When the download completes close all open programs and browsers.
Run MicrosoftFixit50202.msi and choose it's Default mode.

BUT, if the installed antivirus/security suite or a 3rd party firewall is causing the 'read verification error' then the Fixit may/will not work.
If that's the case, then  configure the system to Clean boot after downloading and saving the Fixit.
Then run the Fixit after restarting to the Clean boot state.
Restart and  undo the Clean boot steps, restart once more to normal Windows mode.

NOTE: In the Clean boot state all 3rd party firewalls will be Disabled. When you run the Fixit either disconnect the system from it's net connection or ensure that the native Windows 7 firewall is now On by opening Control Panel > Windows Firewall.