When you move PMS from system to system, Did you perform this step?
If moving from DSM 7 → DSM 7, you put it all in the PlexMediaServer shared folder (after PMS is installed and stopped)
– You then must set the ownership & permissions of the files in the PlexMediaServer shared folder
If moving from DSM 6 → DSM 7, you must put everything in a Plex shared folder. When PMS is installed on DSM 7, it will see the Plex shared folder and convert everything to DSM 7 and move the files for you.
Migrating from DSM 6 → DSM 7
This How-To shows you what you need to do for DSM 7 → DSM 7
As for granting permissions to see your media, System Internal User (not regular user) PlexMediaServer must be given access.