Replacing an individual cable run in a bundle, Need Advice

I have about 30 workstations out of a 1000 that will not get a network connection. The remote networking people tell me the ports keep going into "err-disabled" mode after they're bounced. They say it's happening because a bad cable. I have replaced all cables, except the runs themselves. I have also replaced the desk/wall port. The only thing left is the cable run from the patch panel to the desk/wall port. These cables are bundled and some probably up to 250 - 300 feet. What is the best way to replace an individual cable in a bundle of them? Some go into the tiled ceiling, some go into the floor. Thanks for any and all help.