From the looks of it, you have the hack in place to enable WinMail/OE in WIndows 7??
Code:
Line 4086: 2014-02-19 20:12:18, Info CSI 000003c5 [SR] Repairing 1 components
Line 4087: 2014-02-19 20:12:18, Info CSI 000003c6 [SR] Beginning Verify and Repair transaction
Line 4090: 2014-02-19 20:12:18, Info CSI 000003c8 [SR] Cannot repair member file [l:16{8}]"msoe.dll" of Microsoft-Windows-Mail-Core-DLL, Version = 6.1.7601.17514, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch
Line 4093: 2014-02-19 20:12:19, Info CSI 000003ca [SR] Cannot repair member file [l:16{8}]"msoe.dll" of Microsoft-Windows-Mail-Core-DLL, Version = 6.1.7601.17514, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch
Line 4094: 2014-02-19 20:12:19, Info CSI 000003cb [SR] This component was referenced by [l:242{121}]"Microsoft-Windows-Client-Features-Package~31bf3856ad364e35~amd64~~6.1.7601.17514.Microsoft-Windows-Client-Features-Update"
Line 4099: 2014-02-19 20:12:19, Info CSI 000003ce [SR] Could not reproject corrupted file [ml:520{260},l:66{33}]"\??\C:\Program Files\Windows Mail"\[l:16{8}]"msoe.dll"; source file in store is also corrupted
Line 4104: 2014-02-19 20:12:19, Info CSI 000003d0 [SR] Repair complete
If you undo the hack then that should allow the updates to install.
However, if the hack is not in place - or undoing it doesn't work - then let us know, and we'll deal with the problem.
Please also...
download and save the CheckSUR tool from http://support.microsoft.com/kb/947821
(you'll need to look in the details for Windows 7, downloading from the Microsoft Download Center)
Run it - The tool can take anywhere from 5 mins to a couple of hours to run (or 'Install') depending on how much it has to do, and may exit silently - it may appear to freeze for most of that time, but be patient.
The result is logged in the C:\Windows\Logs\CBS\CheckSUR.log file - and an archive …\checksur.persist.log file
Then zip the CheckSUR.log and upload it to your reply.