Can anyone help

I had a problem with the alarm going off for no reason. The dealer had it in and charged the battery saying it was slightly down. I took no chances and changed the battery. I still have the same problem. Iv just noticed that the little red light in the roof near the mirror is staying on after the engine is switched off. Pressing it does nothing,it just stays on. The only time it goes out is when the engine is running. May be this is the reason for the battery drain. Does anyone know how to reset the alarm or is this some thing else?

Help
Jon