The ballast has two functions. First is to provide the high voltage necessary to strike the arc in the bulb. Second is to regulate the current passing through the bulb.
It takes much less voltage to sustain the arc than it does to initiate and in many types of gas discharge bulbs the voltage required to sustain the arc decreases with increasing current.
Primary symptom of a bad ballast is that the bulb will fail to illuminate.
HID ballasts in automotive applications also differ from home and business applications. Automotive ballasts warm up the bulbs much quicker, 2-10 seconds, where as the arc lamps in my my high school gym from several years ago took a good 10-15 minutes to achieve full intensity.