Computer not detecting my Arduino MEGA 2560 R3
If your Mega has an ICSP header for the USB chip (circled below) then you can test that chip.



You can use another Arduino (eg. a Uno) to detect the signature on that chip, as per my sketch on Sketch to detect Atmega chip types.

All you need is 6 hookup wires to connect your testing board (the known good one with the sketch on it) to the ICSP header on the Mega. Note the pin orientation. I have circled the correct header pins, and pointed to pin 1. On the board pin 1, has a small white dot.

Below are the ICSP pin names, seen from above (component side).





Wire the Uno to the chip being tested as follows:

Arduino Uno      Target chip

D10 (SS)            /RESET
D11 (MOSI)          MOSI
D12 (MISO)          MISO
D13 (SCK)           SCK

Gnd                 GND
+5V                 VCC


Check your wiring! If you wire things around the wrong way you can turn a good chip into a bad one.



Important! Only attempt this process if you can see that you have an ATmega8U2 or ATmega16U2 chip on your board (see below). If you have something totally different this will not work. In that case you probably have a cheap clone board.





Using the Serial Monitor on your Uno, you should then see something like this:

Atmega chip detector.
Written by Nick Gammon.
Version 1.17
Compiled on Jul  7 2015 at 10:47:47 with Arduino IDE 106.
Attempting to enter ICSP programming mode ...
Entered programming mode OK.
Signature = 0x1E 0x93 0x89 
Processor = ATmega8U2
Flash memory size = 8192 bytes.
LFuse = 0xEF 
HFuse = 0xD9 
EFuse = 0xF4 
Lock byte = 0xFF 
Clock calibration = 0xAB 
Bootloader in use: No
EEPROM preserved through erase: No
Watchdog timer always on: No
Bootloader is 4096 bytes starting at 1000

Bootloader:

1000: 0x4B 0xC0 0x00 0x00 0x64 0xC0 0x00 0x00 0x62 0xC0 0x00 0x00 0x60 0xC0 0x00 0x00 
1010: 0x5E 0xC0 0x00 0x00 0x5C 0xC0 0x00 0x00 0x5A 0xC0 0x00 0x00 0x58 0xC0 0x00 0x00 
1020: 0x56 0xC0 0x00 0x00 0x54 0xC0 0x00 0x00 0x52 0xC0 0x00 0x00 0xCB 0xC4 0x00 0x00 
1030: 0x4E 0xC0 0x00 0x00 0x4C 0xC0 0x00 0x00 0x4A 0xC0 0x00 0x00 0x48 0xC0 0x00 0x00 
...


My board had a ATmega8U2 on it, yours might have a ATmega16U2. However the concept is the same. If you see something like that, the chip is (probably) good. At least it responds to programming commands. 



If you see something like 

Atmega chip detector.
Written by Nick Gammon.
Version 1.17
Compiled on Jul  7 2015 at 10:47:47 with Arduino IDE 106.
Attempting to enter ICSP programming mode ......................................................
Failed to enter programming mode. Double-check wiring!
Programming mode off.


Then either you made a wiring error, or the chip is bad.