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.