Electrical issues and questions

[f5fstop]

If that switch light was draining the battery, the remote would not unlock the doors and the radio would not make noise. Assuming the light is an LED, it would take a loooong time for just that LED to run the battery down.
Give me some hints:
Which circuit did you tap into for the power to the switch?
Did the switch require a ground connection for the LED?
Most of these types of switches are two-pole switches. Power comes in on one pole, goes through the switch when the switch is closed (turned On), and the power flows to the lights' relay, energizes the coil, and allows full battery voltage to run to the lights.
When the switch is closed, the LED comes on. That's the type of setup I'm used to.

Sounds like the B+ to the radio is loose (or the radio ground), and when you stepped in, it closes the connection. The noise you hear sounds like a normal initiazation sequence for any radio if it is disconnected from power, and then power is applied. The radios internal memory has to be reset and it has to know how many CDs are inside it.