How to test Arduino board? A little history: I have two Arduino Uno and I couldn't program them by IDE, I got these errors:

avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 2 of 10: not in sync: resp=0x00


So I googled it for a while and I suspect of missing bootloader on atmega micro on the board, as I don't have AVR programmer I programmed both Arduinos with Raspberry Pi and Arduino IDE tool through ICSP pins.

It (burning bootloader) runs perfectly on both Arduino. One of them got fixed and got back to normal, but the other one gave me same error, so I changed their Atmega micro, but same result. Second Arduino (bad one) can't transfer program to AVR even with other one (good one) AVR so both AVRs on the boards are good.
The program (blink LED) run even on the bad Arduino and pin 13 blink.

My questions are:

How could I test the suspected Arduino board? Is the second Atmel micro near usb female port need bootloader too?


  Update 1: I follow this tutorial but my Arduino couldn't go to DFU
  mod by shorting the pins. When I connect those pins led pin 13 not blink and lsusb command show Arduino not Atmel.
  
  Update 2 : I went through this question and this
  troubleshoot to upload bootloader to Atmel USB device but my
  second Arduino (bad one) didn't respond and gave me this error :


Atmega chip detector.
Written by Nick Gammon.
Version 1.17
Compiled on Jul 13 2015 at 11:14:35 with Arduino IDE 105.
Attempting to enter ICSP programming mode......................................................
Failed to enter programming mode. Double-check wiring!
Programming mode off.



  Is it possible my Atmega16U2 chip is burned?
  
  Update 3 : I do reach the point that I am pretty sure Atmega16U2 is
  dead and it isn't responding to its ICSP pins and it blocks any USB to AVR connection. I check the wiring and I
  test it on good Arduino and its sequence are correct and it works on good one. Now what can I
  do, as Atmega16U2 is not rechangeable, should I throw bad Arduino away?
does the built-in arduino LED light up?? If yes try connecting your arduino in another uno usb port or try pressing the reset button on your arduino uno.