I had a similar problem pretty much.
I tried to install solidworks 2016 on my PC but forgot to delete 2015, everything got messed up and when I uninstalled everything and thought I could start at square 1 again during the installation of solidworks 2016 it came up with multiple SQL server errors.
SQL servers are to do with Microsoft not Solidworks, I phoned up Microsoft and they said it would cost around £300 to fix.
Instead what I did was backed up all my stuff onto an external HDD and formatted and re-installed windows on my PC. I then tried to install solidworks and it installed with no problems what so ever.
Please be aware that posting your logs in FULL reveals information such as your software registration number. This could be harmful in the wrong hands. I would strongly suggest that you remove the attached zip file and only give it to authorized SW agents or representatives.