The connector you are showing is for POTS (analogue telephone connection). You cannot use these connectors / wiring for networking purposes.

There is a chance that indeed a wire is running through a PVC pipe from the room where such a connector is present, all the way to your cupboard. If that is so, then you are in luck! You may then be able to replace existing POTS wiring with a CAT5e cable from the cupboard to the room where you intend to work.

The CAT5E cable connects to your modem in the cupboard and also to your PC/laptop.

Now, be careful as replacing wiring is sometimes not possible (if it does not run through a PVC pipe), and even if it is possible, it may not be trivial depending on distance, and the number of bends in the pipe. You would typically fix the CAT5e cable at one end, and pull the cable through. Be sure to do that with two persons; one pulling, and one feeding the CAT5e cable.

Thank you for your reply. So basically I get a long cat5e cable and stick duct-tape to both ends and pull along with another person feeding the cable while hoping it will be in the pvc tube all the way through?

I can give that a try. 

Be aware of the fact that you have to cut off any connectors. They will not fit through the tubing. Before applying the duct tape, strip both cables, so that you can tie the individual wires of both cables together. When you only use duct tape, you run a decent chance of separating the cables somewhere inside the PVC tubing.

You should use solid full copper Cat6 cables when pulling them through electricity tubes and mount them on both sides on a cat6 wall-socket.

Just cutting of the plug from a flexible (non solid) Cat cable is not advisable.