Sounds like a similar problem I was/am having with my computer, and you even said how ****ed up it is.
So you have just upgraded your GPU right? It could be the motherboard if the benchmarks are showing your new card should run the game at much higher FPS.
In cases of mass disappointment, you could always RMA the card. Especially if you've ordered from Newegg. I've done it twice until I figured my motherboard is getting kung fu'd once I get a new pc.
PC hardware is a waste of time and resources the more we go on.
I doubt it is as extreme as yours was. When I got this pc it had a very ****ty quad core in it. When I upgraded to my current dual core, I saw my fps dramatically increase. When I upgraded to the 560ti, I saw my overall fps increase as a result, but the minimum just feels too low. For example when I tried running the Crysis 2 demo at fullHD and extreme settings, it was a slideshow on my 8800gt. 40's fps average with my 560ti is a vast improvement I think.
I think my true real bottlenecks lie in BC2 and Crysis. BC2's fps didn't seem to improve much at all, but it doesn't seem to dip that much either.