Can you please create a restore point then copy the contents of the code box and call it update.reg and then save it to your desktop then right click and then select merge then reboot your machine and check to see if the service pack will install.
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\wuauserv]
"PreshutdownTimeout"=dword:036ee800
"DisplayName"="Windows Update"
"ImagePath"=hex(2):25,00,73,00,79,00,73,00,74,00,65,00,6d,00,72,00,6f,00,6f,00,\
74,00,25,00,5c,00,73,00,79,00,73,00,74,00,65,00,6d,00,33,00,32,00,5c,00,73,\
00,76,00,63,00,68,00,6f,00,73,00,74,00,2e,00,65,00,78,00,65,00,20,00,2d,00,\
6b,00,20,00,6e,00,65,00,74,00,73,00,76,00,63,00,73,00,00,00
"Description"="Enables the detection, download, and installation of updates for Windows and other programs. If this service is disabled, users of this computer will not be able to use Windows Update or its automatic updating feature, and programs will not be able to use the Windows Update Agent (WUA) API."
"ObjectName"="LocalSystem"
"ErrorControl"=dword:00000001
"Start"=dword:00000002
"DelayedAutoStart"=dword:00000001
"Type"=dword:00000020
"DependOnService"=hex(7):72,00,70,00,63,00,73,00,73,00,00,00,00,00
"ServiceSidType"=dword:00000001
"RequiredPrivileges"=hex(7):53,00,65,00,41,00,75,00,64,00,69,00,74,00,50,00,72,\
00,69,00,76,00,69,00,6c,00,65,00,67,00,65,00,00,00,53,00,65,00,43,00,72,00,\
65,00,61,00,74,00,65,00,47,00,6c,00,6f,00,62,00,61,00,6c,00,50,00,72,00,69,\
00,76,00,69,00,6c,00,65,00,67,00,65,00,00,00,53,00,65,00,43,00,72,00,65,00,\
61,00,74,00,65,00,50,00,61,00,67,00,65,00,46,00,69,00,6c,00,65,00,50,00,72,\
00,69,00,76,00,69,00,6c,00,65,00,67,00,65,00,00,00,53,00,65,00,54,00,63,00,\
62,00,50,00,72,00,69,00,76,00,69,00,6c,00,65,00,67,00,65,00,00,00,53,00,65,\
00,41,00,73,00,73,00,69,00,67,00,6e,00,50,00,72,00,69,00,6d,00,61,00,72,00,\
79,00,54,00,6f,00,6b,00,65,00,6e,00,50,00,72,00,69,00,76,00,69,00,6c,00,65,\
00,67,00,65,00,00,00,53,00,65,00,49,00,6d,00,70,00,65,00,72,00,73,00,6f,00,\
6e,00,61,00,74,00,65,00,50,00,72,00,69,00,76,00,69,00,6c,00,65,00,67,00,65,\
00,00,00,53,00,65,00,49,00,6e,00,63,00,72,00,65,00,61,00,73,00,65,00,51,00,\
75,00,6f,00,74,00,61,00,50,00,72,00,69,00,76,00,69,00,6c,00,65,00,67,00,65,\
00,00,00,00,00
"FailureActions"=hex:80,51,01,00,00,00,00,00,00,00,00,00,03,00,00,00,14,00,00,\
00,01,00,00,00,60,ea,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\wuauserv\Parameters]
"ServiceDll"=hex(2):43,00,3a,00,5c,00,57,00,69,00,6e,00,64,00,6f,00,77,00,73,\
00,5c,00,73,00,79,00,73,00,74,00,65,00,6d,00,33,00,32,00,5c,00,77,00,75,00,\
61,00,75,00,65,00,6e,00,67,00,2e,00,64,00,6c,00,6c,00,00,00
"ServiceMain"="WUServiceMain"
"ServiceDllUnloadOnStop"=dword:00000001
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\wuauserv\Security]
"Security"=hex:01,00,14,80,78,00,00,00,84,00,00,00,14,00,00,00,30,00,00,00,02,\
00,1c,00,01,00,00,00,02,80,14,00,ff,00,0f,00,01,01,00,00,00,00,00,01,00,00,\
00,00,02,00,48,00,03,00,00,00,00,00,14,00,9d,00,02,00,01,01,00,00,00,00,00,\
05,0b,00,00,00,00,00,18,00,ff,01,0f,00,01,02,00,00,00,00,00,05,20,00,00,00,\
20,02,00,00,00,00,14,00,ff,01,0f,00,01,01,00,00,00,00,00,05,12,00,00,00,01,\
01,00,00,00,00,00,05,12,00,00,00,01,01,00,00,00,00,00,05,12,00,00,00
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\wuauserv\Enum]
"0"="Root\\LEGACY_WUAUSERV\\0000"
"Count"=dword:00000001
"NextInstance"=dword:00000001
Now if the above does not work then launch Farbar service scanner then type
wuauclt.exe in the search box and hit the search files button.A note pad will appear post the contents of the notepad in your next reply.