1G negotiation requires all wires in the cable to work properly. It's common with non-Cat5E for it to not work, so if the cables are old or slightly damaged, this can happen. If the switch is a cisco (or some other vendors) - it may have a TDR (time domain reflectoromtery) test built in, this will test the cables - https://supportforums.cisco.com/t5/network-infrastructure-blogs/switch-how-to-test-a-cable-status/ba-p/3107543
If you have the ability to test the system while not in production - try plugging the two ports into each other and see if they autonegotiate to 1G or 100M. That would test both of them simulatenously. Also try forcing the switch port to 1G and see if it works.
Hope this helps!
