Unlike the PS3, which accepts all kinds of generic hard drives, the 360 hard drives need to be either authentic ones by Microsoft, or wonky cheap Chinese bootleg drives with modified firmware or something similar.
I'd stay far, far away from the latter ones, ebay has been flooded with these bootlegs and they're likely to be unreliable as f*ck.
If the hard drive is the issue, you can extract a genuine 500 GB hard drive for the slim 360 from its HDD caddy and install it into the caddy of the fat lady 360. It will be accepted flawlessly, provided you've got the system's updates installed. Did that by myself.