My Dell Inspiron 1520 works but the DVD does not respond, the DVD light is not on, the DVD button does not open the draw. Computer Management tells me it is working properly but it is as if it is not getting any power.
Or check it yourself. Since your power supply is (at least mostly) working:
1) Check that the power (and data) cables are still connected to your DVD,
2) If you have a multimeter, check voltage on the power connector currently attached to the DVD,
3) If your Dell has another power connector (ideally on a different cable) try swapping that in.
Unless you've recently been inside your case, the odds are that the DVD player is dead.