Suddently, "avrdude: Device signature = 0x000000" with ArduinoISP. Is my chip dead?
Mostly this error is due to connections/powering issues (as already mentioned in your output ). 


Check connections, especially power and ground also check the
resistance between Vcc and GND of your target MCU. (If it's less than
100ohm that means something is off in your circuitry or your MCU is
already fried.)
Check if your MCU is actually getting enough power (voltage and current) also check if it's getting excess voltage.
Make sure there is proper "common grounding" done between devices.
If you are sure that the above points are checked and you still get the error try the override flag -F (avrdude through shell/command-line) and if you are still not able to upload try the manually changing the address (not recommended ) in your arduino's library so that it matches with the signature it's receiving.
Finally try using a direct USB interface with atmega32u4 as atmega32u4 supports it and upload the bootloader again through an old software called Flip after that try again.


After all this if you are not able to upload then probably your MCU is dead and it might be due to an unnoticed wrong power connection or short circuit or unintentional fuse reconfiguration (highly unlikely).