I hope I can help...
The connector where the power source connects to (ballast input) should all be the same, looks like a 9006 bulb and the 9006 harness should be able to plug right in. (Although it's not recommended because of the initial current draw of the ballast could melt the factory headlight wiring, a wiring kit/harness is preferred.) However, I believe the polarity of the two wires on the ballast are reversed compared to the halogen setup.
The problem you're probably running into is the wire (ballast output) that connects to the HID capsules. If you bought a HID conversion kit, more likely than not you have AMP connectors. This is evident by having two wires with male and female connectors on the ballast and along with the HID capsules. (Most conversion kits utilizes industry standard AMP connectors.)
If you have retrofitted HID projectors into your headlights, you should have the OEM connectors. The OEM ballast connector looks like a round plug/socket at the end. The HID capsule will look more regular bulbs without any wires coming out of it.
The easist way to tell is check your HID capsules. If you don't have any wires attached to it and it unplugs with a round socket/connector, you have an OEM ballast. If your HID capsules have two wires attached to it, you have a modified ballast. There are few eBay sellers that sell rebased 9006 HID capsules that connects with OEM ballast connectors. Hopefully, if you have a modified ballast, the kitting company used AMP connectors.
Xenondepot's conversion kits uses AMP connectors. If you look under OEM HID components, those will be replacement parts for OEM HIDs or if you have a retrofit projector setup. The very first pic, Philips D2S/D2R Plug is the OEM style connector.
FYI, don't power up a ballast without the HID capsule connected to it. It causes the arc to go between the output wire and could fry the ballast.
