There are 2 cables that look identical and the only difference is 2 wires are crossed. One is a normal internet cable the other is a cross over cable. You want a normal cable if you are connecting to a router unless the rooter says otherwise as some single port old one do require a cross over cable.

If you hold both plug from each end side by side look at the colors and if they are the same and in the same place on both plugs its a standard cable.

Do you have an example of both types of cables of how they look like exactly?

I'm not sure how the internet connection was installed, but I'm quite sure that the internet connection was send to a network hub, and from it multiple computers could be connected. Other computers have been connected to it, but I'm not sure what type of cable was used. I don't think that a router is being used.

You may try looking at YouTube - Tiger How-To: Cables To Go Network Cable Installation

this is a video showing you how to create a cable so it gives you full details

Do you still require any help with this matter and update would be helpful