Reading the FRST scan report I noticed that IE10 is on the computer. I was trying to download IE11. I saw a file in the "One Month Created Files and Folders" section named IE11_main.log (From FRST scan report: "2013-12-07 10:12 - 2013-12-07 10:25 - 00008813 _____ C:\Windows\IE11_main.log").
I opened the file and pasted a copy of the log below. Maybe this will help us since that log is the same date the computer would start up correctly. Probably before the last IE11 download attempt. Look at the errors reported.
IE11_main.log
00:00.000: ====================================================================
00:00.141: Started: 2013/12/07 (Y/M/D) 13:12:12.415 (local)
00:00.141: Time Format in this log: MM:ss.mmm (minutes:seconds.milliseconds)
00:00.141: Command line: "C:\Windows\SoftwareDistribution\Download\Install\IE11-Windows6.1-x86-en-us.exe" /WSUS
00:00.359: INFO: Setup installer for Internet Explorer: 11.0.9600.16428
00:00.359: INFO: Previous version of Internet Explorer: 10.0.9200.16736
00:00.375: INFO: Checking if iexplore.exe's current version is between 11.0.9600.0...
00:00.422: INFO: ...and 11.1.0.0...
00:00.468: INFO: Maximum version on which to run IEAK branding is: 11.1.0.0...
00:00.468: INFO: iexplore.exe version check success. Install can proceed.
00:00.468: INFO: Operating System: Windows Workstation: 6.1.7601 (Service Pack 1)
00:00.468: INFO: Trying to extract ID: SetupDownloadList.txt (0) as "SetupDownloadList.txt"
00:00.468: INFO: Trying to extract ID: HardwareBlockingList.xml (0) as "HardwareBlockingList.xml"
00:00.484: INFO: Trying to extract ID: 6006 (0) as "IE11-neutral.Extracted.cab"
00:03.479: INFO: Trying to extract ID: 5501 (1033) as "Spelling_en.msu"
00:03.542: INFO: Extracted Spelling dictionary for en to C:\Windows\TEMP\IE1A592.tmp\Spelling_en.msu.
00:03.542: INFO: Trying to extract ID: 5502 (1033) as "Hyphenation_en.msu"
00:03.588: INFO: Extracted Hyphenation dictionary for en to C:\Windows\TEMP\IE1A592.tmp\Hyphenation_en.msu.
00:03.651: INFO: Trying to extract ID: 6128 (1033) as "IE11-support.cab"
00:21.872: INFO: Launched program to check hardware: "C:\Windows\TEMP\IE1A592.tmp\IE11-SUPPORT\IEXPLORE.EXE" /CheckHardware "C:\Windows\TEMP\IE1A592.tmp\HardwareBlockingList.xml"
00:22.683: INFO: Hardware support check succeeded. Installation will continue.
00:22.683: INFO: Windows 7 operating system detected.
00:22.683: INFO: Service pack major: 1
00:22.714: INFO: Service pack minor: 0
00:22.714: INFO: Service pack name: Service Pack 1
00:22.730: INFO: Version Check for (KB2834140) of C:\Windows\System32\d3d11.dll: 6.2.9200.16570 >= 6.2.9200.16570 (True)
00:22.745: INFO: Version Check for (KB2670838) of C:\Windows\System32\api-ms-win-downlevel-user32-l1-1-0.dll: 6.2.9200.16492 >= 6.2.9200.16426 (True)
00:22.761: INFO: Version Check for (KB2639308) of C:\Windows\System32\Ntoskrnl.exe: 6.1.7601.18247 >= 6.1.7601.17727 (True)
00:22.761: INFO: Version Check for (KB2533623) of C:\Windows\System32\api-ms-win-security-base-l1-1-0.dll: 6.1.7601.18229 >= 6.1.7601.17617 (True)
00:23.167: INFO: Version Check for (KB2731771) of C:\Windows\System32\conhost.exe: 6.1.7601.18229 >= 6.1.7601.17888 (True)
00:23.182: INFO: Checking for correct version of C:\Windows\Fonts\segoeui.ttf.
00:23.494: INFO: Version Check for (KB2786081) of C:\Windows\System32\taskhost.exe: 6.1.7601.18010 >= 6.1.7601.18010 (True)
00:26.333: INFO: Version Check for (KB2888049) of C:\Windows\System32\drivers\tcpip.sys: 6.1.7601.18254 >= 6.1.7601.18254 (True)
00:26.723: INFO: Version Check for (KB2882822) of C:\Windows\System32\tdh.dll: 6.1.7601.18247 >= 6.1.7601.18247 (True)
01:06.878: ERROR: WMI query for Hotfixes timed out. Query string: 'Select HotFixID from Win32_QuickFixEngineering WHERE HotFixID="KB2729094"' Error: 0x00040004 (262148).
01:06.940: INFO: KB2729094 could not be download is not installed.
01:07.143: ERROR: Couldn't create setup troubleshooting shortcut on the desktop. HRESULT: 0x80070002,
01:07.143: INFO: Setup exit code: 0x00009C47 (40007) - Required updates failed to download.
01:08.298: INFO: Scheduling upload to IE SQM server:
http://sqm.microsoft...e/sqmserver.dll
01:13.695: ERROR: SQM Upload failed while uploading "C:\Windows\system32\config\systemprofile\AppData\Local\Microsoft\Windows\Temporary Internet Files\SQM\iesqmdata_setup0.sqm" with error: 2147500036
01:13.695: ERROR: SQM Upload failed while uploading "C:\Windows\system32\config\systemprofile\AppData\Local\Microsoft\Windows\Temporary Internet Files\SQM\iesqmdata_setup1.sqm" with error: 2147500036
01:13.695: ERROR: SQM Upload failed while uploading "C:\Windows\system32\config\systemprofile\AppData\Local\Microsoft\Windows\Temporary Internet Files\SQM\iesqmdata_setup2.sqm" with error: 2147500036
01:13.695: INFO: Cleaning up temporary files in: C:\Windows\TEMP\IE1A592.tmp
01:14.210: INFO: Unable to remove directory C:\Windows\TEMP\IE1A592.tmp, marking for deletion on reboot.
01:14.382: INFO: Released Internet Explorer Installer Mutex
00:00.000: ====================================================================
00:00.063: Started: 2013/12/07 (Y/M/D) 13:24:36.583 (local)
00:00.063: Time Format in this log: MM:ss.mmm (minutes:seconds.milliseconds)
00:00.078: Command line: "C:\Windows\SoftwareDistribution\Download\Install\IE11-Windows6.1-x86-en-us.exe" /WSUS
00:00.078: INFO: Setup installer for Internet Explorer: 11.0.9600.16428
00:00.250: INFO: Previous version of Internet Explorer: 10.0.9200.16736
00:00.250: INFO: Checking if iexplore.exe's current version is between 11.0.9600.0...
00:00.250: INFO: ...and 11.1.0.0...
00:00.266: INFO: Maximum version on which to run IEAK branding is: 11.1.0.0...
00:00.266: INFO: iexplore.exe version check success. Install can proceed.
00:00.266: INFO: Operating System: Windows Workstation: 6.1.7601 (Service Pack 1)
00:00.266: INFO: Trying to extract ID: SetupDownloadList.txt (0) as "SetupDownloadList.txt"
00:00.266: INFO: Trying to extract ID: HardwareBlockingList.xml (0) as "HardwareBlockingList.xml"
00:00.266: INFO: Trying to extract ID: 6006 (0) as "IE11-neutral.Extracted.cab"
00:00.734: INFO: Trying to extract ID: 5501 (1033) as "Spelling_en.msu"
00:00.749: INFO: Extracted Spelling dictionary for en to C:\Windows\TEMP\IE110A.tmp\Spelling_en.msu.
00:00.905: INFO: Trying to extract ID: 5502 (1033) as "Hyphenation_en.msu"
00:00.921: INFO: Extracted Hyphenation dictionary for en to C:\Windows\TEMP\IE110A.tmp\Hyphenation_en.msu.
00:00.921: INFO: Trying to extract ID: 6128 (1033) as "IE11-support.cab"
00:05.382: INFO: Launched program to check hardware: "C:\Windows\TEMP\IE110A.tmp\IE11-SUPPORT\IEXPLORE.EXE" /CheckHardware "C:\Windows\TEMP\IE110A.tmp\HardwareBlockingList.xml"
00:05.975: INFO: Hardware support check succeeded. Installation will continue.
00:06.006: INFO: Windows 7 operating system detected.
00:06.006: INFO: Service pack major: 1
00:06.006: INFO: Service pack minor: 0
00:06.006: INFO: Service pack name: Service Pack 1
00:06.084: INFO: Version Check for (KB2834140) of C:\Windows\System32\d3d11.dll: 6.2.9200.16570 >= 6.2.9200.16570 (True)
00:06.084: INFO: Version Check for (KB2670838) of C:\Windows\System32\api-ms-win-downlevel-user32-l1-1-0.dll: 6.2.9200.16492 >= 6.2.9200.16426 (True)
00:06.100: INFO: Version Check for (KB2639308) of C:\Windows\System32\Ntoskrnl.exe: 6.1.7601.18247 >= 6.1.7601.17727 (True)
00:06.116: INFO: Version Check for (KB2533623) of C:\Windows\System32\api-ms-win-security-base-l1-1-0.dll: 6.1.7601.18229 >= 6.1.7601.17617 (True)
00:06.194: INFO: Version Check for (KB2731771) of C:\Windows\System32\conhost.exe: 6.1.7601.18229 >= 6.1.7601.17888 (True)
00:06.194: INFO: Checking for correct version of C:\Windows\Fonts\segoeui.ttf.
00:06.240: INFO: Version Check for (KB2786081) of C:\Windows\System32\taskhost.exe: 6.1.7601.18010 >= 6.1.7601.18010 (True)
00:06.864: INFO: Version Check for (KB2888049) of C:\Windows\System32\drivers\tcpip.sys: 6.1.7601.18254 >= 6.1.7601.18254 (True)
00:07.005: INFO: Version Check for (KB2882822) of C:\Windows\System32\tdh.dll: 6.1.7601.18247 >= 6.1.7601.18247 (True)
00:48.220: ERROR: WMI query for Hotfixes timed out. Query string: 'Select HotFixID from Win32_QuickFixEngineering WHERE HotFixID="KB2729094"' Error: 0x00040004 (262148).
00:48.236: INFO: KB2729094 could not be download is not installed.
00:48.626: ERROR: Couldn't create setup troubleshooting shortcut on the desktop. HRESULT: 0x80070002,
00:48.626: INFO: Setup exit code: 0x00009C47 (40007) - Required updates failed to download.
00:49.624: INFO: Scheduling upload to IE SQM server:
http://sqm.microsoft...e/sqmserver.dll
00:54.492: INFO: SQM Upload returned 403
00:54.523: INFO: SQM Upload returned 403
00:54.523: INFO: SQM Upload returned 403
00:54.523: INFO: SQM Upload returned 403
00:57.300: INFO: Cleaning up temporary files in: C:\Windows\TEMP\IE110A.tmp
00:57.440: INFO: Unable to remove directory C:\Windows\TEMP\IE110A.tmp, marking for deletion on reboot.
00:57.440: INFO: Released Internet Explorer Installer Mutex