I think that it's more likely that the chip is getting fried due to electrostatic discharge or from a difference in "ground" potentials when it's hooked up.

The cable is hopefully matched to the video impedance, and although it's been noted that's "a lot of capacitance", this is not how a matched impedance cable works! The correct cable should present a constant resistive load regardless of how long it is. This is not like RS232; RS232 has an impedance of about 2000 ohms. Video is usually standard at 75 ohms.

To protect from ESD and voltage differences, from every signal line to ground, put suppression devices. I would use something like the AVX VC060305A1500 TransGuard. If you can get to the traces on the video card, that's great. However if this can't be done, you might be able to build a module from a M/F pair of VGA connectors.

If you're located in North America, I can send a few of the suppressors. They are surface mount 0603. Email me off line.

Finally, once you have this working, arrange so that it's impossible to remove the supression jig from the video card.