Can I get ethernet over this old networking system?

So, I have a workspace in a place that has very old office networking. I’m guessing it’s dating from at least before 2000. My computer is in the other end of the rather large building from the router. I’ve been using the wifi fine but getting slow speeds. So I was wondering if there’s a way for me to get the signal over ethernet to my room using this system.

I don’t know what standard this is and I’ve found nothing online that looks like this. Maybe it’s a standard that doesn’t work with todays Cat5/6 cable but I thought it was worth a shoot.

Picture 1: https://imgur.com/GT6oaN6

This is where the router is stationed. It has a patchbay that has the landline working but no other activity. It’s not labeled so I have no idea what’s going on

Picture 2: https://imgur.com/dERwka8

This is on the other side of the wall. I have no idea how this is interconnected with the other side (pic1). I’m guessing the green labels are the connectors in each room but I haven’t gotten that confirmed.

Picture3: https://imgur.com/pV9RPEZ

These types of connectors are all over the building. They use the standard ethernet connection but I don’t know if it’s an older standard with fewer connections

Picture 4: https://imgur.com/nSIfiHL

There are these “ethernet” to 4 pin sockets around that I plugged into the router room’s bay. Tried to find the connection on the otherside by trial and error connecting it to what number I think is going to my room but no luck.

If anybody has some advice or reference about what’s going on here it would be much appriciated. Or just letting me know that this is a complete waste of time :)

Thanks