I am slightly puzzled by this as the calibration test tones are generated internally by the 568 and thus external cables should have no effect.

I have had almost the opposite problem to you in that expensive digital cables caused dropouts and were very prone to RFI in my system. The thin blue cable seems very good for general use.

It may be that the 568 has been damaged and that pulling the connectors around is making a bad connection internally. I suggest a return to the dealer.

Malcolm