I would first get you battery tested to make sure that its good, Autozone can do it for free. Once the battery is good, then I would check the HID to see if they are wired correctly. Most HID kits are plug and play, requiring no cutting/splicing of the wires. The daytime running lights (DRL) have to be disabled to run HID’s.
Repairing Daytime running Lights. First locate the “Relay Assy. Running Light”. This is located under the dash on the steering column. There are two ways to disable the DRL.
1. Cutting the Yellow wire and grounding the wire coming out of the relay.
2. Cutting the Red with White stripe wire (pin 12).
Depending on which wire was cut, it’s just a matter of reconnecting the cut wires unless the previous owner did something else and really messed things up.
Headlights. I like the advantage of HID’s but if you want to go back to stock, the low beam headlight wire it like this:
The top wire is Red with a Black stripe and the bottom wire is Red.
The Clock. A lot of corolla owners who have this problem will remove the clock and disassemble it to get access to the circuit board. Then take a soldering iron and heat the solder joints to make a better connection. If this fails, replace the clock.
I’m not sure about the air bag light but I do have the factory shop manual and wiring diagram for a 2004 corolla if you would like a copy. Good Luck.