I'm no guru but i've seen this kind of trouble before.
If you also can't hear a chime when the door is open with the key in the ignition (and if you leave your headlights on), a common culprit would be a failed microswitch inside the door lock module. The fix isn't very hard if you're at ease taking the door panel apart and soldering a new microswitch in the module, but it can be tedious/time consuming.
Of course it could be other things, as simple as a bad connection/cut wire... I'll let the experts talk, there are probably other (simpler) causes for this problem.
Edit: Also what ZoomALH said to diagnose the door lock module.
If you also can't hear a chime when the door is open with the key in the ignition (and if you leave your headlights on), a common culprit would be a failed microswitch inside the door lock module. The fix isn't very hard if you're at ease taking the door panel apart and soldering a new microswitch in the module, but it can be tedious/time consuming.
Of course it could be other things, as simple as a bad connection/cut wire... I'll let the experts talk, there are probably other (simpler) causes for this problem.
Edit: Also what ZoomALH said to diagnose the door lock module.