Until the installation of Visual studio 2015, it was always opening Visual studio 2012.
Attached the only error he throws, It seems he was trying to open Visual Studio 2015.
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I have VS 2012, 2013, 2015 installed and faced the same issue. After looking in the Event viewer it was apparent that it was 2015 VSTA causing the issue.
This solved it for me without re-installing everything....
It looks like your installation of Visual Studio 2015 registered itself as the editor for script task instead of what it was before.
What you need to do is make sure the right editor is used again to edit script components.
You could get away with re-registering the correct components for use with script tasks, but it could be needed to remove some registry keys or reinstall your SQL Server tools.
This is not an answer to your specific problem but too long for a comment too.
I have been able to successfully repair a broken SQL Server 2008 using this article: VSTA setup and configuration troubles for SSIS 2008 and R2 installations