I'm not really up to date with bluray, but can I ask why you need to play at 23.976FPS? Is that BR default? I've never seen a graphics card marketed with "can play bluray at 23.976" etc so I'm not really sure if that's common with new graphics cards or not. I've seen many of the new cards sold with lines such as "play your HD DVD or Bluray movies yadda yadda" so I would have thought most of todays cards can handly it just fine. Can any one confirm this?
A quad core with a 9600GT should be more then enough for playing blu ray disks. If you're having issues its more likely to be a software related thing. Try a different player, make sure your computer is free of virus, not having heat related issues, etc.