Is this something that is on all phones, and all co lines? If it is only one phone other than the obvious tel set or cords, maybe it is a bad port on the control unit. If it is all phones on one specific co line, maybe a bad line port on the control unit.
If the customer has just changed service providers, this has the sound of sip trunk problems, or integrated access problems. In this case as Richard has said, the buttset ahead of the system will determine that.