Is it possible to restore database only with .trn files?
Run this:

RESTORE LOG [database_name] FROM DISK = N'path\filename.trn' WITH RECOVERY; GO


Notice I've changed it to WITH RECOVERY - this runs the recovery process and puts the database in a usable state.

Running WITH NORECOVERY leaves the database in a state where further log files can be restored.  This state prevents you using the database until you do a RESTORE LOG ... WITH RECOVERY