yes, see my links below for my OEM HID upgrade for background. Are you sure it is not the HID bulb? Have you tried a new bulb to troubleshoot?
You can get one from ebay for about $100. Just make sure it is from an A6 from 1998-2004 (an A4 or A8 won't be the same; any allroad ballast will work to). Here is exactly what you need:
You can use the other wiring from your old ballas in it's place. Yes, you will need to remove the entire headlight to replace it.