Jamal,
Registering your databases and data directories does not grant the ArcGIS Server account permissions to access your data. You'll need to give the ArcGIS Server account at least read permissions to any folder or database that you register.
Also, your trying to register a file geodatabase which means your supposed to register the folder that it resides in. The dialog to register databases that you're in, is meant for SDE geodatabases. See Registering your data with ArcGIS Server using ArcGIS for Desktop. Grant the ArcGIS Server account permissions to the folder, prior to registering the folder. See Making your data accessible to ArcGIS Server.
Best,
Eric
The data needs to be referenced with its UNC path in order to be approachable internally from everywhere