It may be useful to perform a direct battery test to determine if the problem with your HID kit has to do with a component(s) of the HID kit or with the interface of the HID kit with the stock wiring/electrical system of your vehicle.
To do a direct battery test, the leads/pins that are connected to the stock wiring will instead be touched to the power and ground terminals of a live battery. You can mimic several on-off cycles by simply touching/removing one of the leads. Do the HIDs perform as they were when connected to the vehicle? If so, then the problem is with the HID kit. If the HID kit works fine during the direct battery test, then the problem with the HID has to do with its compatibility with the vehicle. Depending on the particulars, the solution may be to purchase a wiring harness, to check for loose connections, to purchase error code eliminators. If these solutions don't seem appropriate, we'll be glad to advise.
LOW BEAM BULBS
This can be done very easily with low beam bulbs that have metal spade connectors (pins) on the adapter wire (H1, H3, H7, 880, H16, H13 low beam, etc). For low beam bulbs that have plastic shell connectors, either the pins/spades need to be removed from the shell (easier for some bulbs than others; generally strategy described below for the High/Low bulbs) or leads need to be attached to the pins/spades that can then be connected to the battery terminals.
For 9004 H/L, 9007 H/L and H4 H/L bulbs, the direct battery test can be done after the pins are removed from shell connector that is on the harness. Please leave the harness connected to the battery and grounded as originally wired. Please note the position of the wires--color assignments--before removing them from the plastic shell connector.
To remove the pins from the shell connector, you'll need to insert a small screwdriver (jeweler's screw driver, etc) or a pick/awl at the base of the pin on the side of the plug where the pins are protruding. There's a barb that is flared away from the pin that keeps the pin from sliding out of the shell connector. Using the tool, push up on the pin to flatten the barb and at the same time, give a firm tug on the wire from the back of the plug. The wire with the pin will slide out.
After doing the direct battery test, to re-insert the pins, please gently and carefully flare the barb up a little bit so that it will catch as it's supposed to upon re-inserting the pin into the plug.
Unfortunately, H13 H/L bulbs and their harness plug are not amenable to the direct battery test by removing the pins from the shell connector. The only way to perform a direct battery test would be to attach leads to the pins and touch those to the battery terminals.