I already had tried the new WD HDD in another computer, via the adaptor. I got the same result as I did with the Optiplex. Both computers run Windows 7, although the Optiplex is 64 bit and the other is 32 bit. I ran DLG on the Optiplex with the WD HDD connected via the adaptor: it shows my C: drive and the SATA/USB adaptor. Running the DLG quick test on the adaptor gives a pass, but 0 GB capacity (I assume that is not surprising since I don't think the HDD itself is being recognized).
I don't have any other HDDs to try with the adaptor. I do have 2 external (USB) hard drives that connect just fine with the Optiplex. Is there anything else I can do? Worst case, I return the WD and get my money back, but does this mean I will never be able to replace my old HDD?