I have noticed when I turn my HIDs on i get a short whine over my radio while the lights are powering on. This is caused by some electrical intereference comming off the balast. The TIPMs in our cars are easily susceptible to intereference (Possible cause of the starter issue).
I would say probable cause.
HID lights are high voltage devices, your car's electrical system is low voltage.
The ballast contains a DC to AC inverter, and current limiting control for the bulb.
The inverter chops the DC into AC and passes it through a step up transformer to provide the proper voltage to the bulb. Electronic circuits monitor the bulb current and adjust the inverter's output to maintain the proper current through the bulb.
The chopping action draws current from the 12V system is short rapid slugs rather than continuously as if an incandescent bulb were the load.. The TIPM does not like this type of load.
Also, this high current square wave voltage passing through a wiring harness can induce similar waveforms into other wires in the harness (this is called induced voltage). If these wave forms reach the TIPM or PCM inputs, these devices can confuse this electrical noise for a valid signal, and possibly respond in strange ways.
The transformer in the ballast is probably a low-end unit with high magnetic leakage. This means that a fairly strong magnetic field may extend a foot or more from the transformer. As this magnetic field cuts across nearby wires, it will induce the same type of noise mentioned above into those wires.
Finally, the lamp itself is a gaseous arc lamp. Every time the arc restrikes (hundreds or even thousands of time a second), the arc generates "broad spectrum" radio signals. This is called
Radio
Frequency
Interference, this signal can carry many feet in all directions. Every wire crossed by this signal acts as an antenna and sends the interference all over the car's electrical system.
Why don't OEM HID's have any problems?
The systems were designed by engineers, tested and perfected by technicians.
The lamp fixture has proper EMI and RFI shielding
Low leakage transformers are used.
Complex math is used to design the input filter of the ballast.
The ballast is built into a case designed to minimize radiated magnetic fields.
Hardware and software filtering are used to block any spurious signals from getting into the car's electronics.
Proper grounding techniques are used to eliminate ground loops (with electronic systems, a "ground" is not just a "ground" - there is much more to grounding than meets the DIYer's eye)