I'm coming into this really really late, but I'd like to say that your current computer really isn't that weak. If you look at the build in my signature, that one works almost perfectly in every game I play: Battlefield 3, Max Payne 3, Far Cry 3, etc. My graphics card bottlenecks me a little bit, but that's just the VRAM holding back my MSAA settings. I'm actually upgrading to a cheaper and better
660ti 3GB. The bitrate's a little lower, but I think it'll do just fine.
I love the Phenom II x4 965 BE, 8GB of RAM does me just fine, and the Phantom is a great case, plenty of room. I'd say mix and match your two systems; keep the cpu, upgrade motherboard, upgrade the psu, upgrade the gpu, get an SSD.
It would save you tons of money now that can be put towards Haswell, 7-series GPU, a new monitor, or whatever else strikes your fancy in the future.