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It is not a drive related problem. The problem is in the motherboard eSATA hardware. Try a different eSATA port if you have one.
If the eSATA port is bad, you can install an eSATA bracket at the rear of the computer and connect the cable to a SATA port. Then get into the BIOS by repeatedly pressing the F2 key during startup. In the BIOS activate the SATA port that you connected the eSATA bracket. This will work and I have done it on my Dell Optiplex 745 computer.