New receivers automatically shut down because they may be sensing a short somewhere. This short can be internal (within the unit) or external (one of the speakers or speaker wires). The best way to troubleshoot the receiver would be to remove all the speaker wires from the back of the receiver. Then turn on the receiver and increase the volume to the max.
If the receiver shuts down with no speaker wires connected you may have an internal issue. In this case you would need to send it back to the manufacturer.
If the receiver stays on then you need to check each speaker. The procedure is very straight forward. Since you have all the speaker cables disconnected you will be measuring the resistance/impedance of each speaker with the help of a multimeter. Switch the dial of the multimeter to measure Ohms(Ω) and then connect the positive speaker wire and negative speaker wire to the positive and negative poles of the multimeter.
Good Speaker reading between 4-8 Ohms
If the reading is between 4-8 Ohms then the speaker is good. If the reading is 0.1 to 1 Ohms then the speaker is bad or there is a short in the cable. If you have marked the speaker wires then inspect the bad speaker and to make sure that is bad connect a AA to the positive and negative speaker poles. If you hear a popping sound then the speaker is good and you have a short in the speaker wire. Replace speaker or speaker wire and you should be good to go.
Bad Speaker resistance reading