It is common for alarm guys to cut the main ignition switch power wire, they tend to run the alarm power lead between the ignition switch and main power lead for the ignition. It is also common for alarm guys to use butt connectors rather than solder. Most likely the butt connector connection has come loose, or the alarm has failed. Either problem will allow head lights and other items that work from other battery source power to still work but nothing that works on switched power will work. If you pull the steering column covers and lower driver panel, you should see the splice that was done to the ignition switch wiring. You might find a wire loose from the alarm butt connector. The simple test is to bypass the alarm wires that were hacked in, and simply reconnect it like stock.
