Is there a way to reuse ADT's alarm sensors without using their central service?
This sounds like a fun project for a rainy weekend.

I have similar situation.  Bought a house that had an old alarm system in it.  The box is locked and I don't have a key.  The "control panel" still lights up and there is a "ready light" that glows whenever all of the sensors are "happy".

I'm thinking it would be easy to take one of the super-simple wifi enabled micro controller boards out there these days (like the photon/spark unit) and just set it up with IFTTT to notify me if that light goes out when I'm not at home.

Could theoretically make a low-duty-cycle battery powered one that would not even need any connection at all to the alarm system.  Just have the micro controller watch the LED with a light detector.