It's possible in these cases for the provider to disable some of the ethernet ports.
In this case it's perfectly fine to connect a switch one of the LAN ports that works.
I suspect this is happening. They don´t want us to connect many computers on the same account. They always advice costumers that they guarantee internet for 1 computer plugged on the router. Clients must purchase a switch if they want to distribute internet connections. So, my modem/router is connected to a switch, and my computers also. Everything was fine. The problem I discovered recently is that the speed between 2 or my computers is not stable ( 1Gbps ) which should translate as something as 107MB/s copying and writting files from one machine to the other. Sometimes this speed drops to mere 10 or 5 or whatever. Then, I disconnect, reconnect cables, turn off and on the switch, mess with PCs and it returns to normal. I don´t know what´s happening. They are 2 almost identical PCs, i7 2600k, 16Gb ram, SSDs, GTX780, native intel 1Gbps ethernet. One of the PCs has 2 ethernet cards, I once used a cable connected directly from one PC to the other, and got the best speed, but making so, the second PC internet connection becomes dependent from the first one which has internet on the other ethernet port.