|If you're really interested:|
gives you the correct pairing for a CAT5e cable. My guess though is that your cable really is defective because once you switched to another, shorter cable your client could connect. Probably corrosion in a connector.
A new straight-thru cable will set you back ~$15 or you can clean the connectors with baking soda and vinegar, see if that works. Also check the wire pairs to make sure they're inserted correctly and snug. Could be a cut in the middle of the cable though which requires a cable tester to find. I'd just go with the new cable.