FYI,
My old computer had an X2-4800+ which gets a Passmark score of roughly 1300. I also had it overclocked by 20% and it was still hitting 80% usage when used with an HD3870.
Your CPU has a score of 929 which basically would have even bottlenecked my HD3870.
The HD6870 is a far, far better card than the HD3870.
*On the other hand, your CPU is inadequate by itself for most modern games.
My advice is to either:
1) get an HD6770 and find games that run okay with that (try Deus Ex #1, for example, Sam&Max... )
2) Buy an even CHEAPER HD6xxx card for its hardware acceleration (flash video on internet, stored videos). For videos, use K-Lite Standard codec pack and enable "DXVA" and "H.264" and MPEG2" in the MPC-HC video player that comes with it under "Options"-> "Internal filter" (if you didn't check this during setup).
3) buy a new computer.
*I put a $30 AMD HD6450 in my sisters computer. Her old CPU under XP ran at 95% playing 1080p and couldn't do full BluRay at all. It can do full BluRay now and I think usage dropped to 25% for other 1080p video.