As you have said the computer is a bit dated and yes you can overclock the cpu but I don't know if that's going to make the difference that your looking for. The one part that would make the biggest difference is the video card and the one that you have is a bit dated for the newer games and even with a cpu overclock you won't get much of an increase , you will get some but not much. Addinf a newer video card would help but you may have to go higher , maybe a 6770 or 6850. I know it would be more than the 6670 but a lot less than a whole new computer.
You have to remember that yes it's dated but the whole computer is and not just the cpu and video card but the ram and motherboard and possably the psu as well , which wasn't listed and is an equaly important part.
If you want to try overclocking there are stickys at the top of this forum that will help you with some step by step instruction.