After trying to install my WS2003 for testing purposes, I noticed the network driver is failing to be installed.
Also the network adapter was missing from my internet control panel.
So after some looking on the web I found that I needed to use a Legacy Network Adapter in Hyper-V for that machine, instead of the normal one that gets created.
Another thing was then to install the driver for that.
I had to take the driver from another WS2012 R2 virtualized with Hyper-V.
DOWNLOAD the drivers below.
Here you can find that driver: Windows Server 2003 R2 Network Driver
If link is not working, leave a comment, and I´ll have it fixed.