The PSU is not anywhere NEAR powerful enough. All it could support is a 7750. That system would also badly bottleneck a 670. Doesn't make any sense to spend as much on a GPU as you spent on the entire rest of the system.
well, it is a quad core so it should be a bit more future-proof but cant say anything about gaming performance
for your orignal question, it can easily handle a 670 and it an awesome gpu and will last a lot longer than your cpu.
i say u overclock your cpu, it is AMD and easily overlockable if u overclock it it will better.
your cpu may not be THAT bad and if u are not crazy about high FPS u can easily keep it for a year or two, but i would suggest a overlock to get the most out of it.
maybe u should buy a 670 now and replace the cpu after a year or two
well, the BEST cpu for gaming right now is the i53570k, but a regular i5 or in most cases an i3 too, will give u most out of a 670, so it is up to u which u can afford.
what i would suggest u do is get a 670 for gaming and IF u feel it is necessary u can upgrade your cpu later as u wish.
and what resolution do u play in?
1. When a Power Supply is rated at "300W" that means the TOTAL power on all of the Voltage outputs. Not only is that power supply insufficient in raw power (a GTX670 would need a 550W or greater) but you also need to verify the power output on the +12V rail. So you need to ensure:
a) the overall Wattage is high enough (i.e. 550W or greater)
b) the +12V rail Amperage is sufficient (the easiest way is to verify it has the proper 6-pin and/or 8-pin connections for the graphics card), and
c) the needed 6-pin and/or 8-pin connections exist
2. CPU and bottlenecking:
This is somewhat complicated, however by my (very rough) estimate your CPU when paired with a GTX670 would achieve between 50% and 75% the frame rate of the GTX670 when paired with an i5-3570K CPU.
I see THREE main options for you:
#1 - Buy a GTX670 and put it a new build later (not recommended).
#2 - Buy a better CPU and GTX670 (not recommended).
#3 - Buy a graphics card like the HD7850 2GB that isn't as bottlenecked (recommended).
***I want to be perfectly clear, you WILL achieve higher frame rates in some games if you buy the GTX670 versus the HD7850. The problem is that the difference likely won't be huge so the best VALUE is likely to buy no more than an HD7950.
You tend to keep the CPU/motherboard. HD7750/7770 can be your options for basic gaming config. Buying 670 is wasting money due to bottleneck on CPU.
You can consider the ones with 2GB memory from Sapphire and Gigabyte.