How can you test a model 15762536 cy-bg8013zc amp. there is no sound in car stereo

Solution is: replace the fuel injector on #4 cylinder.

I suggest you begin by checking the integrity of the speakers and wiring. This is a fairly easy test to perform and I usually used a pp3 9 volt battery across each pair of speaker wires to ensure each speaker produces a similar amount of crackle and hiss as the wires are wiped across the battery terminals.

Once that test has been performed and found to be satisfactory it is time to connect the wires to the output of the device; radio or amp.

If there is no sound it will be because there is no output from the device. At this point before calling the repair shop it would be a good idea to read the instruction manual to ensure the stereo is being operated correctly.
Good luck!

its a 2011
CY: Y = Yako (Taiwan) C = China. CY is followed by 2-digit year. CY appears on most models produced in China, and is by far the most common form. These forms are apparently associated with the change to Crafted in China, so post-1996 models only would have this form of serial number.
Some Chinese Gretsch's use a CY serial number. http://forums.fender.com/viewtopic.php?t=6299

If the amplifier itself is making the popping sound I suggest you disconnect it immediately, as it could be an electrical short within the amp. If the popping sound is actually coming from the speakers, it could be due to a crossed wire, blown amp channel, or blown speaker. If you posses the technical know-how, you can test the amp channel and speaker by connecting a different speaker to the channel responsible for the popping sound. If the new speaker makes the same popping noise then it is most likely a blown channel. I hope this helps =)

factory amps are located on the stereo unit itself or in the trunk but only if the car was ordered with premium sound and the possibilities of that car being ordered with premium sound is unlikely. so at the harness in the back of the stereo find the speaker wires and hook up a 9 volt battery to the said speakers that dont work if they crackle then its in the stereo if not its the speakers or wires to speakers with battery hooked up and speakers dont crackle go to speaker and test with a vom and test for 9 volts dc

Go to "menu/Setup/Speaker level" and adjust the balance of L-R.See page 21 of the manual:
http://usa.yamaha.com/products/audio-visual/av-receivers-amps/rx/rx-v540/?mode=model

Test your subs on another amp....If they are fine then try running different rcas in your car from the stereo to see if they are the culprit. If still no sound probably your output on your amp is gone.

i would remove the amp and have it "bench tested"
see speakers surrounds if theyre foam and old and falling apart this could be it as well . check amps ground , it must be solid , see power wire to battery and check connection there and to amps it self

To start try disconnecting battery cable for a couple of minutes and see if it can fix the problem.

If this does not fix the problem, then proceed and test the radio connector at the back, checking wiring to speakers.
If there is a factory Amp installed, check amp wiring and re-wire bypassing the Amp to test.

If a stereo unit is correctly wired , there is no external amp, and radio is working but with no sound, that means that you have blown the stereo built in amp final.

this feature is installed already you really should consort to your dealership because this is their expense