Ethernet Not Working in Ubuntu 16.04 – RTL8111/8168/8411 Fix

My wired connection does not work in Ubuntu. I don't have a WiFi card so I need to fix this. I have run some commands to provide some more information(editing this post with results in a few minutes).

I have tried reading through similar questions and answers and nothing I have tried works.

Results:

$ ifconfig -a
enp3s0    Link encap:Ethernet  HWaddr 94:de:80:78:2f:de  
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:10562 errors:0 dropped:2 overruns:0 frame:0
          TX packets:15 errors:0 dropped:730 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:644547 (644.5 KB)  TX bytes:2382 (2.3 KB)

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING  MTU:65536  Metric:1
          RX packets:8708 errors:0 dropped:0 overruns:0 frame:0
          TX packets:8708 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1 
          RX bytes:654867 (654.8 KB)  TX bytes:654867 (654.8 KB)

$ lspci -nn | grep Ethernet
    03:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [10ec:8168] (rev 06)

$ cat /etc/network/interfaces
    # interfaces(5) file used by ifup(8) and ifdown(8)
    auto lo
    iface lo inet loopback

Commands