Open terminal and run commands

inxi -Nn
….. which tells the adapter and driver

Download and install the driver

wget ftp://driver.jmicron.com.tw/Ethernet/Linux/jmebp-1.0.8.5.tar.bz

1. Decompress jme-1.0.8.5.tar.bz2

tar xjvf jmebp-1.0.8.5.tar.bz2

2. Change directory to jmebp-1.0.8.5

cd jmebp-1.0.8.

3. Make and compile driver with root permission

make

sudo make install

The binary will be installed as:
/lib/modules//kernel/drivers/net/jme.ko

4. Load the driver:

sudo modprobe jme

Install ethtool package
sudo apt-get install ethtool

Open terminal and check the eth version
nm-tool
In this computer version is eth4

Run command
sudo ethtool -s eth4 autoneg off speed 100 duplex full

For getting eth up automatically, is needing add the command to the /etc/rc.local file
sudo nano /etc/rc.local

… the contents
#!/bin/sh -e
#
# rc.local
# By default this script does nothing.
ethtool -s eth4 autoneg off speed 100 duplex full
exit 0

Ctr o
Ctrl x

PS. With new kernels like 3.13 driver compiling not working, so the you need to copy /lib/modules/kernel version/kernel/drivers/net folder

The driver can be downloaded from here