Quick update: The cable still works. I tested it on my own PC and it lights up straight away. Still no go in the other PC though. I downloaded Realtek's LAN tester software, and also looked around in the BIOS. Results for the various cable pairs report as:
I'm not entirely sure what this means. Is it safe to assume something is broken on the NIC side? Unfortunately I only have onboard NIC's, no spare lying around to test with.