Your cable in photo #2 should power either of the hand controllers. The new controller powering up with a USB cable to the computer indicates that the hand controller is working. If the old hand controller has a power port so you need to try using the mount's power supply plugged into the hand controller's power port.
The old controller should have two RJ type ports. One is for the update cable, the other for the mount cable. The update port should be too small for the mount cable to fit in it. Check the RJ ports on the hand controllers for a bent connector wire that isn't making contact with the plug when it's inserted.
The Synscan hand controller manual has the pinout for the connector on it that goes to the mount. This should allow you to use some thin wire probes to check the RJ end of the cable you received with the new hand controller to verify that the 12V power is supplied to the correct pins. An alternative to this is to get an RJ11 socket which will give you easier access to the plug's pins by using the back side of the socket where the cat5 (or other) cable is attached.
A final alternative is to locate someone near you that has a Skywatcher mount. You can try your hand controllers on their mount to verify that yours are working properly. A local astronomy club would be a good choice for this.
Edited by Phil Sherman, 13 June 2021 - 11:10 PM.