You can download the service manual at HiFi Engine:
https://www.hifiengine.com/manual_library/nad/712.shtml
When I bought my 712, it arrived broken. Like yours, my preamp did not work. One channel was out on mine. It turned out that the PCB was cracked, breaking the signal circuit for one channel.
In yours, it sounds like both channels are out. That means that something common is preventing the preamp from working on both channels. The common parts include the 12 Vdc power supply to the input selector analog IC (service manual pages 17 & 18) and the part of the preamp circuit between the inputs and the volume control (service manual page 19). I would assume the power supply is working since you have input button lights, but still worth checking.
If you are familiar with basic electrical troubleshooting and have access to a multimeter, you can do some basic troubleshooting to determine where the problem is located. It might be helpful if you tell us your level of experience and knowledge working on equipment.
First, I would confirm that the amp is functional. If you have a cable that connects a source (cell phone, portable device) to an amp (via RCA plugs) set the volume to Zero on the device and connect it to the main in on the back. Connect speakers. I use a signal generator app on my phone as a source. Power up and slowly increase the volume on the source device. You should hear sound from both channels. If the sound is good from both channels, you have verified that the amp is good with both channels.
I suggest downloading the above service manual. Study the schematic and other drawings.
Since both channels are out, I would first check the power supply voltages. Since you verified the amp works, the 30 Vdc rails are good. I assume the power supply would be good because the selector lamps work.
If the power supply is good, you can inject an audio signal into the circuit to see if music makes it to the speakers. I made a simple signal injector using a cable plugged into my phone, a spare capacitor, and two test leads. One lead connected to ground and the other clipped to point in the circuit to see if the signal made it to the amp. I suggest starting at the input to the volume control to see on which side of the volume control the fault lies.