The ballast is used to start and maintain the arc in the HID bulbs. If it's on the fritz, you might have the issues that you described.
Usually when a bulb is about to die, the color of the bulb is pink. If you want to make sure it's the ballast and not the bulb, swap the bulbs and see if the issue is still there or if it followed the bulb.
If you want oem parts, check the catalog of some of the online dealers. I usually use acuraoemparts.com and oemacuraparts.com (iirc from memory).
Usually when a bulb is about to die, the color of the bulb is pink. If you want to make sure it's the ballast and not the bulb, swap the bulbs and see if the issue is still there or if it followed the bulb.
If you want oem parts, check the catalog of some of the online dealers. I usually use acuraoemparts.com and oemacuraparts.com (iirc from memory).