Sorry, I thought you were talking about a 2009 Civic. The 1999 model does not have an immobilizer.
The after market system has a shock sensor, that is triggered when someone bangs on the car. There is a knob on the sensor to adjust its sensitivity. If you set sensitivity to max it will make sound even when someone bumps the car lightly and if sensitivity is set to low, it will not activate at all. So try turning the knob to increase sensitivity. If the sensor sensitivity is correct and you still hear no sound, check the siren and make sure it is working.
As for the blinking LED, may be the previous owner did not install it. It is not really required for the alarm to function. But it recommended to install it because the blinking LED tells you whether the alarm is active or not.