32-Bit Win7 only recognizes 4GB of ram, although from what I have seen this is plenty for gaming purposes.
Your motherboard (bam?
) can take up to 16GB.
Have you tried unlocking the 4th core in your CPU? Not sure if the games you listed even utilize 4 cores, but why not try.
Definitely need to upgrade the "video card" and PSU. I'll go out on a limb here and say that on-board graphics are crap for gaming.
I'd suggest Corsair TX650 V2
(74.99 w/ MiR) and an HD6950 GPU (225-300).
Not really down with AMD graphics so I will let someone else suggest a specific card.
Might want to measure how much room you have between the back of the case and the HDD cage, just to make sure the GPU will fit.
Or, just post which case you're using. mATX board makes me assume mATX case.