The first thing you're going to want to do is figure out what hardware you actually own? You could have an ancient single core P4, but since Windows is reporting 2 cpu's, you have the newer (relative) P4 dual core:
Intel® Pentium® 4 Processors 3.40 GHz - SL7PP
Intel® Pentium® Processor Overview
If you do indeed only have a single core, then you're really going to have to tell me how you managed to fit it onto that motherboard? Scotch, or duct tape?

A socket 478 won't fit on an LGA 775 board.
Either way, you're a gamer trying to run Bad Company at 1920x1080, which given your hardware is an unrealistic expectation; you can't:
Battlefield: Bad Company 2 GPU Performance In-depth > 1920x1200 – High/Medium/Low - TechSpot These benchmarks were done prior to R7 (which gave most users a 20% performance hit), and they were done with a 3.7GHz i7. Since Bad Company is so cpu intense, 10 fps, at 1920, even on all low, is just about what I'd expect from that rig.
It's inexplicable how Afterburner is reporting that you have a 5670? Somewhere, at some point, someone must have downloaded ATI drivers onto that machine. There's really no other explanation... and it also might explain why you're having so many issues now (driver conflicts, mild driver conflicts, but still...).
Uninstall your nVidia drivers. Make sure there's no ATI software to uninstall; if there is, uninstall it (I know you already did, but double check just to make sure). Reboot into safe mode again and run driver sweeper. Check both nvidia and ati. Reboot back into safe mode and run CCleaner:
CCleaner - Optimization and Cleaning - Free Download ( watch the install so you don't install the toolbars and other annoying stuff). Normally you would not have to run CCleaner, but things are so jacked that we want to be sure everything is super clean when you install your drivers.
Boot up normally. Install latest drivers.
Then, and this is most important, get Pops to open up that wallet of his. You need a lot more cpu strength if you want to push that 9600 at 1920x1080. Ideally, you'd like to get a stronger card too, but right now, cpu is probably more important (again, refer to the techspot link for BC performance).
I'm sure you'll be playing BF3. It's also going to use Frostbite, so BC2 is just a preview of the performance you can expect.
**edit**
Oh, and go 64-bit.