Hello LandiC
This has to do with the type of cable and the associated connector wiring. The cable you are using is a patch cable with straight-through wiring. This means that the wires are connected one-to-one from one connector to the other. These cables can be used to connect two different types of devices (e.g. computer and switch). If you want to connect two identical types of devices (e.g. switch to switch) and if I understand you correctly, this is the case for your application, you must use a so-called crossover cable. Here the wires between the plugs are crossed out.

Hello LandiC
Basically, these network cables are backwards compatible and normally there are no such problems with a new, undamaged cable. Since the connection between router and PC works with it, the fault is probably not to be found in the cable. You would have to know what is meant by network distribution (switch, hub, further router), is there an uplink port involved? Is the plug really firmly attached to the distributor? Have you ever tried disconnecting the router and network distributor from the power supply with the cable connected and testing them after restarting? Have you ever tested another port of this network distributor?