Sounds like your external monitor isn't HCDP compliant - disconnect it and see if the DVD will play.  If it will, then you'll need an HDCP compliant monitor.

I don't have an external monitor, only the onboard screen. More confusing...

Are these commercial DVDs, or copies, or home DVDs?

It's commercial DVD's that I have been trying to use.

I had the same problem.  I solved it by downloading Media Player Classic  http://download.cnet.com/Media-Player-Classic/3000-2139_4-10518778.html   

and watch DVDs using this.  Don't know why it works or why media player 11 stopped playing them but this worked for me