If you shutdown and unplug the the network cable when you boot back up is error code 10 still their?
I suggest you try the drivers from Asus as you might have got the wrong ones even if you did get the right ones.
Have you installed the chipset drivers? With -overall command if possible.
Try the motherboard out of the case on some cardboard.
If you still get a error and you done what a asked then the connections from the Ethernet controller to the port is likely damaged and you will have to get a replacement motherboard.