If your SQL Server’s Model database file gets corrupt then the SQL Server itself will fail to start. You cannot run the usual database repair tools when the server services will not even start.

Fortunately, the Model database is just a blank database used as a template for newly created databases. It can be fixed by replacing the model.mdf and modellog.ldf files in the Data folder in the file in the SQL Server folder "C:\Program Files\Microsoft SQL Server\MSSQLxxx\ MSSQL\Binn\Templates".

Then the SQL Server service should start.