Yes, I suspect the "window" surrounding the actual e-sata plug is a bit too narrow on the BDP, preventing full insertion of many standard plugs, leading to a loose (or no) connection.
You might want to try a different cable. Even without getting it to "click" at least I was able to get a signal through on mine. I suspect, even though within specs, the plugs on your CD cable are possibly a smidge bulkier?