You'll need to make sure both graphics card and tv use HDCP (High-bandwidth Digital Content Protection). It's an anti-piracy measure that works by encrypting the signal that travels along the wire. Typically the Blu-ray player software will downscale content to standard definition if it's not satisfied that HDCP is in operation.
A DVI output on a graphics card CAN have HDCP support, but it doesn't have to, so you should check.
<rant>It's been cracked, as would be expected. Now it inconveniences consumers, blocks fair use, creates barriers to entry to the HD software and hardware markets, and obstructs the use of open source software to play HD content. All in an effort to prevent piracy that was doomed from the start.</rant>