As you commented, you got the Atheros Communications Inc. AR8162 Fast Ethernet Controller.
This is some guesswork here because there are several versions of the driver and some people state only one is working for them, I stick with the most popular for now.
First download this file from another machine:
https://www.kernel.org/pub/linux/kernel/projects/backports/2013/03/28/compat-drivers-2013-03-28-5-u.tar.bz2
If you have Ubuntu or another Linux distro on your second machine you can use wget
to download the file:
wget https://www.kernel.org/pub/linux/kernel/projects/backports/2013/03/28/compat-drivers-2013-03-28-5-u.tar.bz2
Next, use your preferred method (preferably an USB Drive) to copy it to your target machine (Toshiba C850) and use the following commands in a terminal. Make sure you are in the right directory first and use cd
to change to the directory where your downloaded file resides.
tar -xzvf compat-drivers-2013-03-28-5-u.tar.bz2
cd compat-drivers-2013-03-28-5-u
./scripts/driver-select alx
make
sudo make install
sudo modprobe alx
If this doesn't work try a reboot first then you can try one of the other versions, I can't tell which will work for you:
Sources (for further reading): This question on AskUbuntu and this thread in the Ubuntu forums.