This finally worked for me: http://klevster.com/fix/sql20122014-management-studio-cannot-find-one-or-more-components-please-reinstall-the-application/
I had to uninstall 2010 shell and then repair MSSMS 2014.
From the link above:
Struck an issue with a Windows 2012 Server with VS2012 installed trying to open SQL 2012 Management Studio giving the error:
“Cannot find one or more components. Please reinstall the application”
After having tried a heap of combination of things, installing SQL 2014 Management Studio, uninstalling, reinstalling… Then repairing VS2012, installing SQL 2014 Management Studio again. All to no avail.
What finally got me over the line was to uninstall the Visual Studio 2010 Shell, this was done by downloading the installer from this link: http://www.microsoft.com/en-us/download/details.aspx?id=1366
Once downloaded, run the installer and remove the VS2010 Shell component. Once done, run the SQL 2014 Management Studio installer or do a repair on your existing installation, this will itself reinstall the VS2010 Shell components.
Then bam, it finally opened for me.