*Edit* Oops I see you know what 169.blah is - just ignore anything you already know
That 169.x.x.x address is what windows sets when it's set to DHCP but can't get an address. Okay, so the router is known good, the cable is known good.
A couple of things to check.
1. Is it a crossover cable? If your other devices support autosense, they will "reorient" themselves to connecting, whereas your GX260 may not be able to do this.
2. Does the port have bent pins?
3. Can you set your ip manually, another computer's ip manually, and then be able to ping each other? They will need to be on the same subnet - best to choose ip's like 10.0.0.1 and 10.0.0.2, mask of 255.255.255.0, and leave the rest blank. Then try to ping one from the other (you should use a crossover cable for this! Or go through a hub/switch, NOT a router! If this works with the "known good" cable you may have a crossover cable, or one device at least supports autosensing...)
4. It could be software - odd if you've reinstalled. A guy at work had a laptop that "somehow" got set to 10mbps rather than auto. I have no idea why. Assuming you have the proper full intel drivers (if I remember rightly, for a GX260, it's a pro 100/ve? Download from intel.com...), just check through all the panes and make sure you don't see "10mbps half duplex" or something silly on network speed.
If it does odd stuff with known good pci network cards as well, I would suggest the motherboard may be slightly knackered. Something about the southbridge (I think that'd be the right place for onboard ethernet as well as pci stuff). Or it might be something in the bios.