I've sometimes found that ensuring that the earlier IE is fully updated, and then also installing and updating IE9/10 this can help get IE 11 installed.
Having said that, I don't believe it'll work here - you have some weird errors in the background CBS data, despite both SFC and CBS being clear...
Code:
2014-08-31 11:37:22, Info CSI 00000163 Couldn't find the hash of component: Microsoft-Windows-IE-DataWarehouse, Version = 11.2.9600.16428, pA = PROCESSOR_ARCHITECTURE_INTEL (0), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral in the catalog [l:192{96}]"\SystemRoot\WinSxS\Catalogs\beffec19b64becec82c3c141b4f260a62c486738233893ae2f064146620c5994.cat".
2014-08-31 11:37:22, Error CSI 00000164@2014/8/31:18:37:22.804 (F) d:\win7sp1_gdr\base\wcp\componentstore\csd_winners.cpp(1302): Error 80092004 [Warning,Facility=FACILITY_NTSSPI,Code=8196 (0x2004)] originated in function CCSDirectTransaction::AddImplicationsToCatalogsAndVerifyComponentHashes expression: (null)
[gle=0x80004005]
2014-08-31 11:37:23, Error CSI 00000165 (F) 80092004 [Warning,Facility=FACILITY_NTSSPI,Code=8196 (0x2004)] #550006# from CCSDirectTransaction::PrepareForCommit(...)[gle=0x90092004]
2014-08-31 11:37:23, Error CSI 00000166 (F) 80092004 [Warning,Facility=FACILITY_NTSSPI,Code=8196 (0x2004)] #550005# from CCSDirectTransaction::ExamineTransaction(...)[gle=0x90092004]
2014-08-31 11:37:23, Error CSI 00000167 (F) 80092004 [Warning,Facility=FACILITY_NTSSPI,Code=8196 (0x2004)] #550004# from CCSDirectTransaction_IRtlTransaction::ExamineTransaction(...)[gle=0x90092004]
2014-08-31 11:37:23, Error CSI 00000168 (F) CRYPT_E_NOT_FOUND #549756# from Windows::COM::CPendingTransaction::IStorePendingTransaction_Analyze(...)[gle=0x80092004]
2014-08-31 11:37:23, Error CSI 00000169 (F) CRYPT_E_NOT_FOUND #549233# from Windows::ServicingAPI::CCSITransaction::ICSITransaction_Commit(Flags = 38 (0x00000026), pSink = NULL, disp = 0, coldpatching = FALSE)[gle=0x80092004]
2014-08-31 11:37:23, Error CSI 0000016a (F) CRYPT_E_NOT_FOUND #549232# 4565338 us from Windows::ServicingAPI::CCSITransaction_ICSITransaction::Commit(flags = 0x00000026, pSink = NULL, disp = 0)
[gle=0x80092004]
2014-08-31 11:37:23, Error CBS Exec: Failed to commit CSI transaction to resolve execution chain. [HRESULT = 0x80092004 - CRYPT_E_NOT_FOUND]
2014-08-31 11:37:23, Info CSI 0000016b@2014/8/31:18:37:23.295 CSI Transaction @0x3c85618 destroyed
2014-08-31 11:37:23, Info CBS Perf: Resolve chain complete.
2014-08-31 11:37:23, Info CBS Failed to resolve execution chain. [HRESULT = 0x80092004 - CRYPT_E_NOT_FOUND]
2014-08-31 11:37:23, Error CBS Failed to process single phase execution. [HRESULT = 0x80092004 - CRYPT_E_NOT_FOUND]
There's a couple there that I don't ever recall seeing before, but I believe they indicate that the SoftwareDistribution files are corrupt.
Have you tried download the offline installer and using that?
Download Internet Explorer 11 (Offline installer) - Internet Explorer