HIDs will pull way more than 35W at startup, so say they are rated at 35 watts or 3 amps each, they will probably pull twice that when firing, so 12 amps, and I believe the stock fuses are 10A.
Have you tried firing the headlights, letting them warm up then firing the fogs?
Have you tried firing the headlights, letting them warm up then firing the fogs?