Getting File not found error doing point in time database restore in SQL Server 2008
When you open that dialog, SQL Server populates that windows with a lot of backups for the history of backups taken for that database. This history is stored in msdb and is not synchronized with the file system, so it is possible that the backup files themselves were deleted  or moved already.

Instead of restoring from that history, select to restore from disk and pick the file(s) yourself.



Restoring a Backup

You need to first restore a full backup. That restore has to happen without recovery. 

Then, if you have one, restore the latest differential between the full backup and the point in time you want to restore to. this also has to happen without recovery. 

Finally, you need to restore all log backups between that differential (or the full if you didn't have one) and the point in time you want to restore to. Those log backups need to be restored in chronological order, also without recovery. The final log backup you can restore with recovery to bring the database back online.

SQL Server does not force a specific extension for any backup type. Most likely you will have .bak for full backups. Differentials might be either .bak or .dif. For log backups I have seen .trn, .log and others. Some people don't use extensions at all for their backups.

But it is probably a safe guess, that your .trn file is a log backup, so you will need additional backup files to restore that database.