Recovering a SQL Server database
The last successful restore was the RESTORE DATABASE. Since you specified NORECOVERY, the database is, as expected, in restoring state. If you don't have any more backups to restore and just want to get out of the restoring state, you just do:

RESTORE DATABASE mydb WITH RECOVERY


That's it.  You find the database as it were when that full backup you restored was produced.

As for log backups, you need an unbroken chain of log backups. You can't skip a log backup, like you most probably tried to do. You likely got an error message saying that the log backup was too recent to restore, citing LSN numbers and that it requires some earlier log backup with some earlier LSN number. There's no way around the "unbroken chain of log backups" requirement. If you can't find those log backups, or a more recent full backup, then you are probably stuck with a 4 month old database.