I have the same RTL8111/8168B PCI that you do-
The only way that I was able to get a good working internet connection was I had to purchase a Linksys USB Adapter and then installed a driver.
My Desktop now communicates with my wireless modem and all is good.
One place you can look for a driver is on the Realtek website:
If installing a driver for your PCI Express card doesn't help check your interface file found in this path:
Check that wired is not commented out and wireless is commented out-
You can edit that file with Nano or your favorite text editor.
Not sure but you may need the firmware:
In my case my interfaces file and the arguments in it supported both wired and wireless-
I had to comment out wired with # at the beginning of the argument in the file and than I was able to connect via the internet-
Hope this helps-