No wired ethernet connection

I would start at the bottom of the stack and confirm that the Ethernet device is actually getting detected by the OS first.

Example

$ sudo lshw -c network -sanitize
  *-network               
       description: Ethernet interface
       product: 82577LM Gigabit Network Connection
       vendor: Intel Corporation
       physical id: 19
       bus info: pci@0000:00:19.0
       logical name: em1
       version: 06
       serial: [REMOVED]
       capacity: 1Gbit/s
       width: 32 bits
       clock: 33MHz
       capabilities: pm msi bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd 1000bt-fd autonegotiation
       configuration: autonegotiation=on broadcast=yes driver=e1000e driverversion=2.3.2-k firmware=0.12-1 latency=0 link=no multicast=yes port=twisted pair
       resources: irq:43 memory:f2600000-f261ffff memory:f2625000-f2625fff ioport:1820(size=32)

From this type of output you can start to confirm that there is an actual driver attached to your Ethernet device and that's at least getting detected by the kernel during boot.

UPDATE #1

Based on this output from your updates:

$ sudo lshw -c network -sanitize:
  *-network NO RECLAMADO  
       descripción: Ethernet controller
       producto: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller
        ...
       fabricante: Realtek Semiconductor Co., Ltd.
       id físico: 0
       información del bus: pci@0000:04:00.0
       versión: 06
       anchura: 64 bits
       reloj: 33MHz
       capacidades: pm msi pciexpress msix vpd bus_master cap_list
       configuración: latency=0
       recursos: ioport:d000(size=256) memoria:d0004000-d0004fff memoria:d0000000-d0003fff

You should notice that the "configuration" line doesn't specify a kernel module (driver). This is likely your issue.

I did find this thread which sounds related to your issue (even though it's with Ubuntu). The thread is titled: "Thread: 13.10 RTL8111/8168/8411 slow internet". I'd try loading this module to see if it'll work with your particular hardware:

 $ sudo modprobe r8169

You can check the output of dmesg afterwards to see if the module loaded successfully.

If this works you can make it permanent by adding this module to you system's list of modules to load at bootup.

 $ sudo echo "r8169" >> /etc/modules

You could also add an association in the /etc/modprobe.d/ directory which would associate the device, r6168 with the r6169.

I had this problem on Linux Mint 17.3 The drivers are current. went to network connections and deleted the ethernet connection. then added a new one and set the eth 0 interface to "Require IPv4 addressing for this connection to complete" . Then setting IPv6 Settings to "ignore". Came right up.

The info from "sudo modprobe r8169" and "dmseg" helped ID the problem when it complained about nss- hostname and that IPv6 was not ready.