Go to the Maxtor / Seagate website and look for their free package of HDD diagnostics. Download and follow the instructions. Usually there are several versions - one that runs under Windows (suited to your situation), one that you burn to a CD so you can run from it independent of Windows (very good for lots of times), etc.
Consider removing the HDD unit from the external case and mounting it (even temporarily) as an internal HDD connected directly to the mobo, then see if it works. Sometimes the problem is the case interface electronics, not the HDD itself. And you might find that the diagnostic utilities work better for an internal drive.
What you describe sounds like it is not reading the Partition Table correctly. If it turns out here is nothing wrong with the hardware itself, then you might need a utility for Partition Recovery.