It should be easy enough to shine a light into the DVD player and see if the disc is in there. If it is not in there then we have what we call in the manufacturing industry "operator error". Is it possible that the disc was removed and you forgot about it? The only other thing that comes to mind and you did not mention is if the DVD player has room for multiple discs. I got one from my son in law years ago that held 5 discs. But I have never seen one of those connected to a computer.

One last thing to try is to put another disc in and see if it plays.