I have gone through your Error log file. As per your Error log file your System data has corrupted. Mainly in your case 'Model' database. as per your log error shown like
66.2015-10-14 09:31:04.68 spid12s Error: 9003, Severity: 20, State: 1. at line number 66 in your error log.
As per Gail Shaw Blog :-
If a model file is corrupt, then we need to restore a backup of model. Let's see what Books Online has to say about restoring model:
"Restoring model or msdb is the same as for performing a complete
database restore of a user database."
For Ref : - https://www.simple-talk.com/sql/backup-and-recovery/the-sql-server-instance-that-will-not-start/
If a model file is missing, we need to find out what happened to it. Has a drive not come online (or come online after SQL started)? Has someone accidentally renamed or moved the file? If we can make the model files accessible to SQL Server, in a similar fashion as described previously for the missing or inaccessible master files, then this will solve the problem.
Let's try starting SQL Server from the command line, with traceflag 3608
This will prevent recovery of all databases except model. This will 'Clearing tempdb database' and 'Starting up database 'model'.
Since the problem seems to be the clearing of TempDB.
let's go back to the beginning and try to restart SQL Server, but this time with traceflag 3609.
This time SQL Server won't even start. We specified via use of traceflag 3609 that SQL Server should, on startup, recover TempDB from the existing files but not attempt to clear it.
you can also ref http://www.dbforums.com/showthread.php?1203681-Error-9003-Severity-20-State-1 and https://support.microsoft.com/en-us/kb/822852#/en-us/kb/822852 for clarification.
NB:- In case of production databse , Before doing any troubleshooting you must consult with system Administrator and DBA Team. Always keep all backup file in safe zone.