Arduino is perfect (assuming you have one unused) Set a pin as output and connect it to your chosen pin on the cable, set lots of pins as inputs and connect them to the cable starting at the other end. Loop through checking the inputs (or use interrupt pins if you have enough) and print the pin name when it goes high. Then you can press keys and record them in a spreadsheet with the number of the output pin on the cable down the side and input across the top with the key names in the middle.
Hopefully all the rows are at one end and the columns the other, that would make it easier.
Actually would this be automated? Connect every pin on the cable to a pin on the arduino, press all the keys by putting something heavyish on the back of it then set each pin high and scan the others. You wouldn't know which key was where but would have the rows and columns.