Nerrad, I'm certain that your CPU is bottlenecking your card heavily, I had the same processor and even my 6770 was running slower than my old X1950 Pro, I recently upgraded to a Phenom II x4 and now it works as well as all the videos I watched suggested it would.
With a 6870 the effect would be even more noticeable, so I'd look into upgrading your CPU ASAP as opposed to mucking about with the card or returning it.
No, if you replace the motherboard then you just have to do a phone activation.
I asked all over the Dell forums and every single user I spoke to said that after replacing the mobo in a Dell prebuilt you would either have to buy a new OEM key or new retail copy, it's the same deal if you try to replace the original HDD, Dell PC's no longer come with an OS CD or Key, you have to use the backup partition on the stock HDD to revert it if anything goes wrong, not to mention that all OEM copies are SINGLE use only and most if not all prebuilt PC's use OEM copies, even if you bought it yourself you cannot get the key reset no matter what you do.
So yes, he would have to buy a brand new copy