"Can I play a Blu-ray disc in my computer DVD player?
The short answer to your question is you can only play Blu-ray media in your computer DVD player if that DVD player is a Blu-ray drive. If standard DVD players supported Blu-ray playback our entertainment options would be far easier. Instead special hardware is required for Blu-ray. Think of the leap from DVD to Blu-ray as something similar to the leap from a standard CD player to DVD. A DVD player can typically also play CD media, but a CD player can't play a DVD. Blu-ray presents a similar problem. For playback on your computer, there are additional challenges beyond just having the right hardware.
Additional Requirements for Watching Blu-ray
In addition to needing a Blu-ray drive attached to your computer, you also need several additional features before you can watch a Blu-ray movie.
HDCP Support is required from both the video card on your computer and the monitor you connect to the video card. The rules are slightly different for desktop and laptop systems.
HDCP and Desktops: If the video card has an HDMI connection, you can generally assume it also supports HDCP. In some cases, DVI-out on video cards also support HDCP, but this is very inconsistent. Checking with the support site for the video card manufacturer is about the only way to know for sure. If your video card only includes VGA connections, you will need to upgrade your video card to watch Blu-ray movies with your computer. Monitors are a little trickier, since they often don't make it obvious whether there is HDCP support or not. VGA-in on a monitor will not support HDCP, in most cases DVI-in will. Your safest route is a monitor with HDMI-in. In an ideal configuration, going from HDMI-out on your video card to HDMI-in on a monitor will keep Blu-ray playback headaches to a minimum.
HDCP and Laptops: In general, laptops manufactured in 2007 or newer have a secure video path with support for HDCP. This is not true across the board and there's often no way to tell for sure without connecting a Blu-ray drive and attempting to watch a movie. Laptops built before 2007 often don't have a video card with enough video processing capability to playback Blu-ray movies, so not having HDCP support is generally a non-issue for older hardware.
Blu-ray Software is also need to watch Blu-ray movies on your computer. I use Cyberlink PowerDVD for Blu-ray playback on my computer, which is currently the most viable option. PowerDVD includes an application to help you troubleshoot whether your components are Blu-ray compatible, which does make the whole process less frustrating.
In summary, to play Blu-ray movies on your computer you need: a Blu-ray drive, an HDCP compliant video card, an HDCP compliant monitor, and software with Blu-ray support. Once you have all those pieces, in theory your Blu-ray movies will play smoothly.