Opening the ie7.log file, near the end I found the error message.
75.609: DoInstallation: Installing assemblies with source root path: c:\fb18136b310872b2d2275c9e\
75.609: Num Ticks for Copying files : 13390
85.250: DoRegistryUpdates:UpdSpInstallFromInfSection Failed for ProductInstall.GlobalRegistryChanges.Install error: 0x5
85.250: INF_REGISTRY Failed
85.250: DoInstallation:DoRegistryUpdates failed
85.297: Access is denied.
85.312: Internet Explorer 7 installation did not complete.
Select 'OK' to undo the changes that have been made.
85.312: Starting process: C:\WINDOWS\ie7\spuninst\spuninst.exe /~ -q -z
135.531: Software Update Rollback has completed with return code 0xbc2. This rollback requires a reboot.
135.531: Internet Explorer 7 installation did not complete.
Internet Explorer 7 has been partially updated and may not work properly.
135.531: Update.exe extended error code = 0x5
I am going to try to check Microsoft's site a bit better to see if I can find a solution, but I doubt that I will find one. Can anyone help me?