Electrical – Difference between blue and grey blue coaxial ports

First obvious problem- you haven't wired it correctly. You have proven connectivity works with the long Ethernet cable so the fact you are failing to get lights shows that you need to sort this.

Also getting signal on all the wires shows something is connected somewhere. Could be a splice as Steven mentioned, or some other problem. Is it even cat-5 cable?

In general what I do is use the existing wire as a pullthrough and replace it with known good cable.

Yes, with it being cat-5e cable, you could repurpose it as network cable by installing rj-45 jacks. Early Ethernet (10mBit & 100mBit) used two pairs (4 wires) and Gigabit typically uses all 4 pairs (all 8). Your Cat-5 link is referring to 10/100 Ethernet, so only two pairs are used. The other two pairs could carry a phone line each or another Ethernet connection (we used this on IP phones, the computer was on one half and the VOIP on the other half, figure out the color diagrams yourself for your RJ-45s on the second half). My preference is to not muck around with this as the first time you plug in a Gigabit equipped computer, you face getting full ring voltage into its RX/TX for the second set of pairs. Wire it for Gigabit using all pairs and be done with it.

In the good old days of 25 wire straight cable, daisy chain was common installation technique, with the advent of CAT-4 and above phone installations I have worked with have all been star to a central patch panel.