I ran into this error this week and was able to get past it without having to reinstall the OS, which is apparently a feat.
I found this message in the Detail.txt log file:
2015-07-23 15:48:39 Slp: Sco: Attempting to install MOF file
2015-07-23 15:48:39 Slp: Running: C:\Windows\system32\WBEM\mofcomp.exe "C:\Program Files (x86)\Microsoft SQL Server\100\Shared\sqlmgmproviderxpsp2up.mof"
2015-07-23 15:48:39 Slp: Microsoft (R) MOF Compiler Version 6.0.6000.16386
2015-07-23 15:48:39 Slp: Copyright (c) Microsoft Corp. 1997-2006. All rights reserved.
2015-07-23 15:48:39 Slp: File 'C:\Program Files (x86)\Microsoft SQL Server\100\Shared\sqlmgmproviderxpsp2up.mof' not found!
2015-07-23 15:48:39 Slp: Sco: Compile operation for mof file C:\Program Files (x86)\Microsoft SQL Server\100\Shared\sqlmgmproviderxpsp2up.mof failed. Exit code 1
After that, I uninstalled SQL following the steps outlined here (with the exception of step 8, which is a utility for Windows XP and is deprecated):
http://blogs.msdn.com/b/sreekarm/archive/2010/03/15/sql-express-is-not-installed-properly-steps-to-be-taken-before-reinstall-again.aspx
After that, I started the install again. I clicked through all the dialog boxes up until the point that it was about to start the install. Then, I copied the following two files from a known good SQL installation:
C:\Program Files (x86)\Microsoft SQL Server\100\Shared\sqlmgmproviderxpsp2up.mof
C:\Program Files (x86)\Microsoft SQL Server\100\Shared\1033\sqlmgmprovider.mfl
After that, I got past the MOF Compiler error in the SQL install. I did get another error that caused me to have to copy the following files as well:
C:\Program Files\Microsoft SQL Server\100\Shared\RsFxInstall\RsFx0100.inf
C:\Program Files\Microsoft SQL Server\100\Shared\RsFxInstall\RsFx0101.inf
C:\Program Files\Microsoft SQL Server\100\Shared\RsFxInstall\RsFx0102.inf
C:\Program Files\Microsoft SQL Server\100\Shared\RsFxInstall\RsFx0103.inf
C:\Program Files\Microsoft SQL Server\100\Shared\RsFxInstall\RsFx0104.inf
C:\Program Files\Microsoft SQL Server\100\Shared\RsFxInstall\RsFx0105.inf
I'm not sure if this was related or not, but after doing the clean uninstall, copying all 8 of the files listed above, then re-starting the install, it worked. Hope this helps someone.