10 Windows updates not installing Error 80073701

You have obviously run the CheckSUR/SURT tool - please post its logs.
C:\Windows\Logs\CBS\CheckSUR.log and CheckSUR.Persist.log

Here's one of the reasons we need it!

Code:

2015-06-16 08:15:46, Info                  CBS    Exec: Installing Package: Package_30_for_KB2982378~31bf3856ad364e35~x86~~6.1.1.0, Update: 2982378-83_neutral_GDR, InstallDeployment: x86_3e7c4b8a4e0ee119d1049df8294325a0_31bf3856ad364e35_6.1.7601.18270_none_7cd6f84541f36b2b
2015-06-16 08:15:46, Error                 CSI    00000209@2015/6/16:15:15:46.877 (F) d:\win7sp1_gdr\base\wcp\componentstore\csd_locking.cpp(324): Error STATUS_SXS_ASSEMBLY_MISSING originated in function CCSDirectTransaction::LockComponent expression: (null)
[gle=0x80004005]
2015-06-16 08:15:52, Error                 CSI    0000020a (F) STATUS_SXS_ASSEMBLY_MISSING #5335645# from CCSDirectTransaction::OperateEnding at index 0 of 1 operations, disposition 2[gle=0xd015000c]
2015-06-16 08:15:52, Error                 CSI    0000020b (F) HRESULT_FROM_WIN32(ERROR_SXS_ASSEMBLY_MISSING) #5335530# from Windows::ServicingAPI::CCSITransaction::ICSITransaction_InstallDeployment(Flags = 0, a = 3e7c4b8a4e0ee119d1049df8294325a0, Version = 6.1.7601.18270, pA = PROCESSOR_ARCHITECTURE_INTEL (0), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral, cb = (null), s = (null), rid = [77]"Package_30_for_KB2982378~31bf3856ad364e35~x86~~6.1.1.0.2982378-83_neutral_GDR", rah = [2]"17", manpath = (null), catpath = (null), disp = 0)[gle=0x80073701]
2015-06-16 08:15:52, Info                  CBS    Failed to begin deployment installation for Update: 2982378-83_neutral_GDR [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CBS    Failed to execute item[0] in Package: Package_30_for_KB2982378~31bf3856ad364e35~x86~~6.1.1.0, Update: 2982378-83_neutral_GDR [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CBS    Failed to execute execution update. [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CBS    Failed to execute execution package: Package_30_for_KB2982378~31bf3856ad364e35~x86~~6.1.1.0 [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CBS    Failed to prepare execution. [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CBS    Failed to process component watch list. [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CSI    0000020c@2015/6/16:15:15:52.431 CSI Transaction @0x18dd670 destroyed
2015-06-16 08:15:52, Info                  CBS    Perf: InstallUninstallChain complete.
2015-06-16 08:15:52, Info                  CBS    Failed to execute execution chain. [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Error                 CBS    Failed to process single phase execution. [HRESULT = 0x80073701 - ERROR_SXS_ASSEMBLY_MISSING]
2015-06-16 08:15:52, Info                  CBS    WER: Generating failure report for package: Package_for_KB3004375~31bf3856ad364e35~x86~~6.1.3.1, status: 0x80073701, failure source: Execute, start state: Staged, target state: Installed, client id: WindowsUpdateAgent

You posted a shortcut rather than the file. Please try again.

on that case you have something pruning out log folders on every boot - you'll have to stop it doing that if we're to have any chance of fixing this problem (or any other problem for that matter!

Run the CheckSUR tool again, and post the new CheckSUR logs before rebooting.

Here's the summary from the latest run...

Code:

Summary:
Seconds executed: 1079
 Found 51 errors
  CSI Missing Winning Component Key Total count: 51

This indicates fairly massive registry corruption - possibly caused by a registry 'cleaner' or similar 'optimizer' utility.

The only thing I can recommend at this point is a repair install - or failing access to the necessary media, a full reformat and reinstall using Recovery system.

If you don't have a 'retail' Windows disk, can you borrow one? Otherwise you're likely to be limited to doing a Recovery to ex-factory condition using your machine's built-in Recovery media

See here for the repair instructions - Repair Install