Internet explorer only works when run as administrator

Found a ton of virus files? No anti-virus is perfect and once a computer has been compromised, there is no telling the damage. You should probably run at least 3 different anti-virus programs to catch what others have missed. If possible, consider a factory restore to original condition.

Already did...

Open command prompt and run sfc/scannow

Did that - a few times.

Does running this command at prompt work for you? Please post results.
DISM.exe /Online /Cleanup-image /Restorehealth

I tried this in safe mode.  Windows 7 DISM did not like the command line switches

Hmmm.
Try running superantispyware free version. Reboot. Let us know results.
http://www.superantispyware.com/superantispywarefreevspro.html

What antivirus do you have? Does it support a boot scan? If so run that also.

Is there anything in your event logs?

Sorry you didn't mention if you tried uninstalling and re installing.

I uninstalled and reinstalled - from Programs/Windows Features.  I used MalwareBytes (14 day trial - most recent) and I used M$ Essentials.  Did not run stand alone, but both found a bunch of problems and both fixed them.  I scanned until "clean".

What was the result of superantispyware?

>>  Malwarebytes found a ton of virus files  <<  in such a case - don't waste more time on it, you'll never be sure it is clean
backup  - and do a fresh install
you can use the windows cd for install - or use the restore partition to do so

**when starting the install from CD - be sure to wipe the partitions

I was not clear on a few things.  1)  I reinstalled IE10, not the O/S.  2)  I have not had a history with Super Anti spyware, so I will avoid that for now.  Malware bytes and M$'s software should do the trick.  Frankly, my thinking was that a folder or file(s) had their permissions adjusted.  I have no idea what they should be set to.  One post suggested disabling UAC, which I suspect would solve the problem but throw the baby out with the bathwater as IE would now be wide open to future attack.

I have decided a different approach that will likely work for sure.  I am going to upgrade the PC to Windows 10.  The owner of the laptop gave an immediate "yes" when asked.  Sadly, we'll never know the answer to this problem....

Thank you for your help.

Troubleshooter was the first thing I ran.  It failed to find anything..Usually, it is pretty good it getting the easy stuff, but I really think it is a folder/file permissions issues.  Only the developers know that answer.  The user is now on Windows 10 and it works like a charm.  I know there are privacy settigns that can be turned off.

Hmmm.  I don't see the close this case button...