there's a real possibility that the servo (the rectangular blue box) on that feed no longer works, or the probe is stuck. Unfortunately it does not look like it's easy to reach. Also the risk is that if it's stuck, it might have broken when trying to turn. You might need to get a ladder and a screwdriver and check it. Star by removing the feed cover, to expose the probe, and look at it while someone changes the polarity on the controller, and see if it turns (a small mirror makes this a bit easier)
As far as electrical signal, there should be 3 wires: 0V(ground), 5V permanent, and pulse (I think that's the white wire). The way the servo works is that it reacts to the pulses, and its position is proportional to the width of the pulse (i think it's also called duty cycle?). This can be easily checked if you have an oscilloscope. The 5V and the pulses should be there permanently.
As far as controlling this servo, you can either build a small circuit with a timer like a 555, and control it manually. Or you can get more sophisticated and build a circuit that will detect the voltage that your receiver sends to the LNB and use it to control the previous circuit, which would make it automatic. Rick Satellite sells something like that, but it's out of stock. Last but not least, you can try to find an old receiver/positionner (usually from the analog days) and use that to control the dish position and the servo. Of course that also means it's not automatic. Of course the ideal solution would be an ASC-1 from Titanium, but it got discontinued recently and it would have dented your limited budget a bit. So for now maybe stick with your antenna concept controller as least until you figure out what's wrong.
Another option is to completely replace that old feedhorn with an LNBF. But that's something I would recommend only for C-Band. I would not recommend a C/Ku combo LNBF.