SP 1 fails to install, but no error message.

I have been working on my friend's Dell laptop running Windows 7 Home Prem. It keeps informing me that I have one critical update (Service Pack 1) when I install it, it says the update was successful, but the next time I reboot, it gives me the same critical update message. If I look in update history it shows that it has been successfully installed 4 times. If I go to system in control panel it shows that I'm running Win 7 Home Prem, but no mention of SP 1. as it does on my desktop. I hid the update to stop it from nagging all the time. I tried to update to IE 11 but it downloads, but will not install because it says I have the wrong version of Win 7. I ran sfc /scannow. It said it couldn't repair all files, but somethings do run better, just can't run the update. I have run 4 anti-virus scan with different software including RogueKiller; Nada. What's next? I've run out of smart.

Thank you for your prompt reply. Here are the issues: I had already downloaded and run the SURT. The Hotfix that it sought to install was already installed, so it would not continue and I got the following; installation encountered the error 0x80240009. I ran sfc \scannow and have attached the CBS zip. Spoke too soon. This happened:
500 - Internal server error.

There is a problem with the resource you are looking for, and it cannot be displayed

Second Reply.

I rebooted the computer and ran SURT again. This time it installed; I received no error messages. I ran SFC again and am attempting to attach zip file.

500 - Internal server error.

There is a problem with the resource you are looking for, and it cannot be displayed.

Will attempt to zip individual files and upload.

500 - Internal server error.

There is a problem with the resource you are looking for, and it cannot be displayed.

It appears the zip file is too large.

I am attempting to attach this zip to see if it is helpful.

Attachment 303518

Thank you. Try this.

Attachment 303532

Attachment 303547