Tom,
Seems like a small cable to provide the signal path to the Aladdin, but it may. I have seen them used before for thermostats and the like. If your Aladdin still reads current properly and the cable is a plug like a phone line, you could check the AC current at the Aladdin, shut off the Aladdin, disconnect the cable, turn the Aladdin back on and see if the current reading goes away. If it does then, I would assume, that this is the signal cable you are looking for. It should be connected at the other end to the Aladdin display. I would pull the display and pull the plugs and reinsert then a couple of times at both ends to renew the contacts. If that does not work, then the next step would be to find a female receptacle for the phone type plug that has some wires on it and measure at the Aladdin end of the cable that you see the two 12V AC sources that are being fed into the Aladdin. If 12V is not there, then the cable is a problem. If the 12V is there, then the display circuitry is faulty. It may be a phone line type plug, or if it is a little larger but a similar style, it may be an Ethernet plug.
I have never had to work on one of these systems so I am no expert. Hope I'm not leading you down the garden path with my logic......just letting you know what I would be doing if it were me.
later Ed