Sounds like what you need is a very simple accelerometer switch.
Think of a small conductive tube, maybe 5-6mm diameter. Mount it upright, perhaps on a copper sheet or bare PCB. In the center of the tube, mount a small metal spring with a weight at its top and the bottom securely fixed to the same plane as the tube. Do not let the spring and tube come into contact, the spring/weight should be electrically isolated. Attach one wire to the base of the spring and one to the tube.
Whenever the device is moved, the mass of the spring and weight will damp its motion and it will touch the inside of the tube. The electrical connection will give you an indication that the device has been moved.
Cost = pennies, Build time = 30 minutes.
Brian.