As said above, on 2001 Omegas the boot can not be opened while the key is in the ignition (very annoying - I have a 2001 car) which is supposed to be safety feature preventing you from acidentally opening the boot while driving, so this may be the problem. From 2002 onwards, Vx apparently replaced the need ot have the key in the ignition with a delay on the button action - you need to press it for a few seconds before the boot opens.
As for the alarm button, what it does is de-activate the cabin volumetric motion sensors, in case you are leaving a dog in the car. The way to use it is by pressing it just before leaving the car, you then have 15 seconds or so to leave the car and activate the alarm using the key fob.
Having said that, from what you describe you may have an electrical problem under the central console around the radio area, so it is possible that some of the buttons in this area are either diconnected or get no juice.