Schematic Diagram

The photocell has a very high resistance in the dark which drops very low when the door opens and the light turns on. The 22 uF capacitor begins to charge and when the voltage reaches the zener voltage, the beeper sounds. Closing the door allows the capacitor to discharge through the 10 meg.  resistor, resetting the beeper. The schema draws very little power when the door is shut and only draws significant current when the beeper is sounding. The transistor may be a single NPN darlington such as the MPS-A14 or two 2N4401s connected as shown. Other types will also work. The delay may be changed by changing the value of the capacitor. It may be a good idea to add a 10 uF capacitor across the battery.