ERROR : The log scan number (85:368:1) passed to log scan in database 'model' is not valid. This error may indicate data corruption or that the log file (.ldf) does not match the data file (.mdf). If this error occurred during replication, re-create the publication. Otherwise, restore from backup if the problem results in a failure during start up.
I have done just to solve this:
Step-1: Go to this path
C:\Program Files\Microsoft SQL Server\MSSQL10_50.SQLEXPRESS\MSSQL\Binn\Templates
Step-2: Copy and paste the database/file named model.mdf and modellog.ldf to this path
C:\Program Files\Microsoft SQL Server\MSSQL10_50.SQLEXPRESS\MSSQL\DATA
Now, service will be started !!!