When you installed TRS06, did you follow all installation instructions and after installation of TRS06, did you configure it proper with your TRS04 user name, user number etc.? Did you install TRS06 with a different name (say, TRS06 or such) to a different partition on your hard disk?
If you did all correctly, perhaps you have a bad install of TRS06 and you could always uninstall it and re install it again and see if anything has changed for the better. You also have to let CMP in TRS06 know all your details like user name, number, log on details etc. for CMP to reach the DLS or it will not function.
If you uninstall TRS06 and reinstall it again, this is the time to apply Service Pack 1 (SP1) on a new install if the version of TRS06 you have is not yet upgraded to it.
Rereading your post, do you use CMP to d/load from the DLS? If it is configured properly (look in its options/configuration), it should log on and TRS04 should never get in its way.
Re you are not seeing any TRS06 items when manually searching, all you need to do (if searching) click on TRS06 in the content box as well and perhaps d/load items without DLHelper(04) or CMP(06) and d/load the items directly via FTP as a .cdp file. Info of how to do this is on the DL page of the item you would like to d/load. That way if installing the .cdp file, you can direct it to the TRS version you want it for and keep the .cdp file as a backup as well.
*Edit: Did you register TRS06 with AURAN too?
Cheers
VinnyBarb