How can I modify telephone Cat5 cables and jacks into Ethernet 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.