2003 Mercedez Benz C240 Alarm
Cup your hands around the lock and breathe on it.
A common solution is to heat the key with a lighter, then while it is still hot, put it into the lock. The heat from the key should thaw out the lock. I don't know why your father won't let you heat the key up. It he isn't there, then he won't know you did that unless you tell him. To prevent further problems, you should use some lock de-icer and spay that into your locks. Or you can try a little bit of liquid graphite, followed by some WD40 or silicone spray.
Not so much a draw issue as it could be a wiring issue. If the alarm was aftermarket, it could conceivably be send false signals to the cars ECM, which then disables the ignition circuitry. I had a car with an aftermarket system and I ripped it out, because it kept the car from starting every so often.
Bring a lighter and burn your key for a minute or so. Otherwise, hold the flame to the keyhole directly. And try multiple locks, even if you can crawl through your trunk.
