Might be the module fucked my other half had the same problem that started like your's. The light was on when the car was on then went off when you turned the car off it was like this for ages then one day it would'nt start at all i disconnected it from the module and is started stright up so like i say might be your module on it's way out If you do disconnect it your alarm wont work at all so might be worth getting another module and trying that if you need the alarm to work if you aint got an aftermarket alarm fitted