How can I backup & restore a single FILEGROUP in Sql Server 2008
You need to restore the transaction logs so that you have a consistent database.  Currently the filegroup which you have restored is at a different point in time than the rest of the database.  Once the logs have been rolled forward and everything is consistent then you can bring the database online.

If you look at the data in the msdb database you'll be able to see which transaction log files you need to restore in order to bring the database online.

There's nothing wrong with your backup and recovery syntax.