I'd be curious to see what the actual link speed is between the two endpoints, rather than a speed test out to the ISP. Are you able to do a speed test with something like iperf3 locally?
I have old cat5e and it can do 10Gbps - Wondering what you're hoping to see here? If the endpoints negotiate 100Mbps then thats the top speed of the link - could be the endpoints (worth trying others) but chances are its the ends that are bad, not the middle unless you're pounding nails in where the cables go.