According to the logs your using a CE database but its trying to connect to a SQL Server…
Make sure you did not delete the CE components from your computer.
PS: Alternatively you could convert the .sdf to SQL and install SQL Express this is the preferred method.
That is the key btw. Either its trying to find a .SDF file that does not exist anymore or the CE components are uninstalled. CE is absolutely horrible and you should try to convert to SQL and use either SQL Express or LocalDB SQL.
Here is a tutorial to show how to convert your CE .SDF file to SQL: