The BH12LS35 is an internal drive, not a player. Your title is a bit confusing.
The Radeon HD 6670 should be fully compatible with high definition video, and the models I’ve seen have HDMI and HDCP enabled DVI outputs. What software do you have that is saying this card in not sufficient?
You need good software to playback blu ray video on a pc. What are you using? Most drives come with PowerDVD, which will work if updated, but isn’t my favorite. I much prefer Arcsoft TotalMedia Theater despite its cost.
See if you can get the movie to play using a free player called Media Player Classic HomeCinema: http://mpc-hc.sourceforge.net/ You won’t get the menus, but you should be able to play the main movie with this software.