could be an ignition switch, also, just because a battery reads 12 volts, doesn't necessarily mean it has the AMPS to do the job.... a bad battery can still read 12VOLTS... good luck :)
Check the headlight switch, if not it's probably a fusible link in the headlight circuit.
Check fuses and the headlight switch.
Look at your realys next to your battery and check them all
even if you disconnect the battery the headlights stay on????????????? check the headlight switch
Use a wire tester and check everything from the light switch to the headlight assembly. If there's no voltage at te headlight switch, then trace it all the way to the battery.
Check the fuse/relay panel box adjacent to the battery, under the hood.
That's what I would check first. If the battery checks good, make sure battery cables are tight. Also check the fuse.
Check battery if low could trigger alarm.
Check your battery terminals, when it has enough power to run the starter, then suddenly not its probably a loose or corroded battery connection.
Check to see if your battery is secure. in my jetta the battery kept sliding forward and smacking my left headlight because it was not tightened down
The battery was week and stopped recharging. Check the date of the battery! The batt feeds some electricals directly...Flat batt could stop engine from running.
Most electrical components also use a relay so check for one, then check the headlight switch itself. The switch will tell the motors to activate via the relay.