The headlight switch was replaced under warranty when the previous owner had the car. It still doesn't rule it out, but juist food for thought. In typical troubleshooting fashion, think about what conditions changed when the problems came up. (stereo install) The alarm's been in the car for six years, so I would say the problem's not from the alarm. Besides, the alarm wires are tapped into the car's wiring, so it couldn't interrupt the circuit for the lights. The fact that the lights blink when you arm the alarm would indicate the lights do in fact work and the power is being supplied. From that point, I'd double check the switch.
A couple of people asked 1) if you used a wiring harness to connect the radio, and 2) did you try unplugging the radio to see if it fixes the problem. I didn't see an answer, so I'm guessing you didn't check it yet.