salam abu...

it is a good news that your screen goes blank when you shift to reverse - it means that the logic operates fine.

Now you need to troubleshoot the camera and the video feed.

1. check the voltage that comes to power wires for the camera - use voltmeter to check the voltage;
2. if the voltage is present, check for the video signal coming out the camera - you can use a small TV, or a computer monitor that has an RCA input - on some chinese cameras the video output is an RCA plug that is black and can be confused with the power plug - connect the video output from the camera to that monitor (i use a special test monitor that is 4" and runs off a battery);
3. if you have video coming out of the camera, test the video cable between the camera plug and the video module and see if the video comes out the far end of the cable;

Can you perform these tasks?