I took a look at the Golden Eye kit.? I see that they use the (very old) Hella HID ballast.? This ballast dates back to the 90's, but remains popular for the aftermarket because customers generally don't have very stringent demands for a robust product.? So why is this important?...
That ballast unfortunately did not meet the GM specification for Radiated Emissions (part of the EMC requirements).? It was actually pretty bad, so Philips developed a power source to meet the requirements (first use '99 GMC Envoy, then the design progressed from there).? Even though the ballasts may have a Philips label (LVQ 212 is the part number)? on them, they are actually a Hella product (not a Golden Eye product, they just added their sticker).
What do try...
I don't have the '04 lighting schematic burned in my head like I do the '02, but it may make a difference where you place your power and ground.? And shielding may help.
Power, I'm assuming that you are using a relay driven from the original headlight wiring (if not, do this).? Grab power directly from the underhood Bussed Electrical Center (on an unused accessory feed).? If? you're not using a relay, I'd strongly suggest it.? Make the power feed run as short as you can.
As for ground, on the 2002 vehicles the ground side of the Low beams went back into the IP harness and connected to the Multifunction Switch (turn signal, cruise, wiper, etc) before being grounded inside (yep same ground as the radio - #1
.? That's why, at least on 2002 vehicles, you shouldn't replace the HID system without a relay (you don't want to inrush and startup current to go that far to ground, it acts like an antenna).? Check the 2004 schematics and find out where the ground side of the bulb goes.? If it is shared with the radio, that's trouble.
Shielding - in someone's infinate wisdom (sometimes called wisdumb).? They got rid of the shielded jacked between the bulb and ballast.? If you can, shield the high voltage wiring from the ballast to the bulb.? ?Make sure the ballast case is grounded.? It's easy to try aluminum foil to start, then use something more robust (like copper mesh or something) for the long term.
Question...? During startup, the ballast will drive the bulb at about double the power to get it up to 70% brightness in 3 seconds (a requirement).? After that, there will be a time of what is called "runup" that will last 10 to 60 seconds at less current.? After that, the bulb should be in steady state.? Start the system up (with the radio on) and note if the interference decreases from initial start to steady state.? That may help diagnose the problem.
Good luck...