Excellent. What we need is to hook that 3x2 header up next to the USB. They are numbered different than chips:
(MISO)1 - 2 (Vcc)
(SCK) 3 - 4 (MOSI)
(RST) 5 - 6 (Gnd)
...where the little silk screen dot indicates Pin 1. For reference, you were shorting Pins 5&6 to reset the Atmega8u2/16u2.
Upload Nick's programmer to your working Uno:
This will be the programmer. It will verify the connections by identifying the chip. We will have to switch to Arduino as ISP when we get to the AVRDUDE stuff.
Anyhow, hook Pin 1 of the Target to D12 of the Programmer Pin 2 to 5v, Pin 3 to D13, Pin 4 to D11, Pin 5 to D10 and Pin 6 to Gnd.
Plug the USB into the Programmer Uno, open the serial monitor and select 115200 baud.
Copy and paste what you get here.