Here's how to get the Notto SE 9007 Bi-Xenon kit to work perfectly in your 03+ Cavalier. (mine is an 04 Sedan LS)
Link to kit: http://www.carid.com/2004-chevy-cavalier-xenon-hid/notto-hid-kit-342713.html

--Disclaimer--
Following these steps is what made this kit work in my car! I don't guarantee that it will make yours work, or that you wont damage any of the wiring or electronics in your car! I accept ZERO responsibility for any damage that may be caused by following this quick-fix!!!!
Also, please install your HID lightbulbs into aftermarket or custom made projector housings, or find a way to modify your stock housings!!! HID's inside of the stock housings blind oncoming drivers!!!

1) Before you even attempt to hook up the HID kit, have your DRL disable finished. The low power of the DRL circuit will short out the Ballasts. (or at least it did for me, but CarID graciously replaced them)
Link to DRL Disable: http://www.j-body.org/forums/read.php?f=7&i=326113&t=326113

2) On the harness that goes in between the stock headlight 9007 socket and the ballast, look for a black heat-shrink-wrapped item. Cut the heatshrink off, but do not damage anything under it. Under there will be a diode sitting in a socket that allows you to just pull the diode out. Pull it out, making note of the silver banded end of the diode and which wire (red or black) that its connected too. Re-install the diode in the REVERSED position, so that the Silver banded side of it is not opposite the side it originally was.

Now wire your kit up to according to the manufacturer's instructions, and enjoy your new HID set-up.

The Reason you have to reverse the diode is that most cars switch the Positive wire that the headlamp uses to switch between HI and LOW. The 03+ cavaliers, for whatever reason use a switched ground to accomplish their HI/LOW switch.

I forgot to say this, but the CarID Kit also comes with inline error code cancel devices. Don't use these, they go *boom*. If I had read the little piece of paper that came with them, it states that they are for cars with digital headlight controllers.... and our beloved Cavaliers and Sunfires don't have those.

Forgot this too.... you MUSE use the Relay harness if you want this to work properly... if not, when you hit the Highs, those little tiny little 20 gauge wires that go to the above-mentioned diode will be the only things powering the highs, and you will toast them!