In so far as cables are concerned, in general, they are difficult to repair.
The first step is to test each line (wire), do a continuity test, this would involve a multimeter preferably with a buzzer on the diode function.
If the line is continous, then the buzzer would sound. You have to do this on all lines, you may have more than one line/wire broken and in several places, too. Even if the buzzer sounds the line may still be faulty, otherwise known as an intermitent fault.
The best approach is to conduct the manufacturer or retailer of the chair and ask for a replacement cable or email me direct at:
george@www.com
George, September 2007