The two larger plugs go into the ballast. The smaller plug is to power the solenoid that moves the HID tube to create the "low" and "high" beam.
It's hard to tell who the kit is by, but it looks similar to a lot of "bi-xenon" kits I've seen. You'd probably be better off just picking up an entirely new kit, since the replacement parts are likely difficult to source (much like your entire kit's origin).
If you need headlights right now, you could pull the HID setup, and put some halogen bulbs back into your car.
www.retro-solutions.com has been a good source for HID kits, around here, if you're looking to get another HID setup.