Hi MWillesen,
Welcome to Microsoft community where you can find all the answers related to Windows.
As per the description, you tried to install Windows updates manually and it ended up in error
C:\WINNT\system32\muweb.dll. The specified module could not be found.
What is the kind of update or KB article that is failing to update?
Method 1: Run the Windows update troubleshooter
Open the Windows Update troubleshooter
http://windows.microsoft.com/en-US/windows7/Open-the-Windows-Update-troubleshooter
Method 2: You may reset Windows Update components.
How do I reset Windows Update components?
http://support.microsoft.com/kb/971058
Note: This section, method, or task contains steps that tell you how to modify the registry. However, serious problems might occur if you modify the registry incorrectly. Therefore, make sure that you follow these steps carefully.
For added protection, back up the registry before you modify it. Then, you can restore the registry if a problem occurs. For more information about how to back up and restore the registry, click the windows help article below.
Method 3: System File Checker [SFC]
If still you are facing the issue, then you can try running a System File Checker [SFC] scan on the computer which will replace the missing or corrupt files & check if the issue persists.
How to use the System File Checker tool to troubleshoot missing or corrupted system files on Windows Vista or on Windows 7
http://support.microsoft.com/kb/929833
Method 4: To re-register DLL files, run the fixit:
http://support.microsoft.com/kb/956708
Note: The steps apply to Windows 7 also.
Post back with the result. If the issue is still not resolved, I’ll be glad to provide additional options.