1) Is the eSATA port a shared eSATA/USB port?
2) Is the drive eSATA only or is it a eSATA/USB drive?
If you answer yes to both of those question, then you are having a similar or same problem as I am. I have a Toshiba with a eSATA/USB port. If I connect a eSATA only device to the port it works fine, if I connect USB to the port it works fine. If I use a eSATA cable and connect to a eSATA/USB external drive, it does not work at all.