OK, a few things:
So your parking lamps are always on when the car is in gear (just the fronts) and also the headlamps? Can you turn off just the headlamps with the override switch? On my GXP I only had headlight DRL's and I could turn them off with the AUTO override or by turning on the fogs.
If you have DRL's in the headlamps (as well as the parking lamps) did you ever attempt to turn them off or override them when you had the HID's installed? I imagine if you left them on the HID's would have just flickered hopelessly when the DRL's were on which would clearly damage the ballasts as well.
Finally, I don't think that the turnsignal switch, or any other switch is the problem. I say that because you said that the parking lamps wouldn't work even with them coming on automatically at dusk. If fuses keep blowing there is a short somewhere in the electrical system or there is a problem with the headlamp's lighting module.
If you could answer the above questions it would help and in the meantime I will go to my local GM dealership and get a wiring schematic for your DRL's and see what I can find out. Those schematics helped my eliminate my DRL's on my 01 Aurora.