Moved Model Database and now my SQL Server doesn't work
Did you follow the steps in the documentation for doing this?

Move System Databases - SQL Server 2012


  To move a system database data or log file as part of a planned
  relocation or scheduled maintenance operation, follow these steps.
  This procedure applies to all system databases except the master and
  Resource databases.
  
  
  For each file to be moved, run the following statement.
  
  ALTER DATABASE database_name MODIFY FILE ( NAME = logical_name , FILENAME = 'new_path\os_file_name' )
  Stop the instance of SQL Server or shut down the system to perform maintenance. For more information, see Start, Stop, Pause, Resume,
  Restart the Database Engine, SQL Server Agent, or SQL Server Browser
  Service.
  Move the file or files to the new location.
  Restart the instance of SQL Server or the server. For more information, see Start, Stop, Pause, Resume, Restart the Database
  Engine, SQL Server Agent, or SQL Server Browser Service.
  Verify the file change by running the following query.
  
  SELECT name, physical_name AS CurrentLocation, state_desc
  FROM sys.master_files
  WHERE database_id = DB_ID(N'&lt;database_name&gt;');
  
  
  If the msdb database is moved and the instance of SQL Server is
  configured for Database Mail, complete these additional steps.
  
  
  Verify that Service Broker is enabled for the msdb database by running the following query.
  
  SELECT is_broker_enabled 
  FROM sys.databases
  WHERE name = N'msdb';
  
  
  For more information about enabling Service Broker, see ALTER
  DATABASE (Transact-SQL).
  
  2. Verify that Database Mail is working by sending a test mail.


Critically, note that the command you ran doesn't actually move the physical data files.