Hi John,
It sounds like the geodatabase you received may be corrupt - try requesting it again.
Tell the dataset creator to zip the entire geodatabase directory, from one level above the the files you're seeing.
Eg, if the file is called C:\data\FileName.gdb, they should open C:\data in Windows, right-click on FileName.gdb, and zip this. This will create a zip file containing FileName.gdb, which will contain the constituent files.
You should be able to preview the geodatabase in ArcCatalog, or add it to ArcMap using the Add Data option.
Steve