Just a thought and suggestion.
You have i5 3470 Quad with benchmark of 6573 and I have AMD Phenom II X4 965 BE overclocked with current benchmark around 5100, add to this GTX 660 from MSI, now I am able to play Battlefield 4 on high settings, Far Cry 3 on almost Ultra, Battlefield 3 was everything ULTRA etc.
Why do you need new build? You need stronger video card and this is it.
Now, considering what I just said above, do you still want the most for your buck below $150?
I know there is GTX 750 and maybe even GTX 750 TI, which will work on in your PC without upgrading PSU (GTX 750TI require 60 watt only) for under $150 before taxes and shipping, would you consider that?
Your turn.
P.S. If you go with even stronger card, you can do much more, but more money...