Oooh, bummer.
Hmm, well IF I did get 64-bit then I had 4 gigs of 667 RAM, then would it be like a killer gaming system even if I only had an okay 256mb graphics card and a 2.33 or 2.4 dual processor?
No, it will not be a "killer gaming system", you need a better graphics card for that. Mouse Ace's wish list on newegg is pretty much a "killer system" in my opinion, although it could have better parts if money was no object (e.g. 8800GTX 768Mb, QX6700 instead of Q6600). The 4Gb of RAM will make a difference over 2Gb, but I'm sure sure how big a difference, as I don't run 4Gb of RAM.
On your budget, I don't think you would get a "killer system", I'd say you need at least $2000 for that, maybe more - Ask Nick N, he will make your budget go far.
Also, what dual core are you looking at? I'm guessing the 2.33 dual core is an E5500 and the 2.4 is an E6600. If this is the case, then the E6600 is a better CPU (in my opinion), although you may be better spending a little more ($30 or so) and getting the E6850 CPU. It has a higher FSB (1333MHz), which will allow for faster RAM frequencies (I think), and it has a higher clock speed of 3.0Ghz. If you get this, try for 2Gb DDR2 800Mhz RAM. DDR3 RAM is out now, and is faster, but is also very expensive

Triple_7 from these forums has an E6850, and when I asked him about it, he said it was good, so I don't think you would be dissappointed

Basically, for it to be a killer system, all the components have to be high-end. A high end CPU and RAM won't make a killer system if you have a lousy graphics card.
Remember - Today's high end components will soon be outperformed by the newer Intel and AMD processors, and DDR3 RAM. If you want to make the most of your budget, do what I am doing an wait until after Christmas (Around January). you will pick up a much better system for your money.
Note: If Nick N answers, ignore all I said, he knows more, so listen to him

Edit: Just saw your edited post, 3Gb of RAM runs on 32 bit, so yes you could do that but RAM works best in matched pairs, so I say you are better off with 2x 1Gb sticks or 4x 1Gb sticks, not mixing with 512 sticks to get 3Gb. Also, if you don't want to spend $200 or more on a video card, you are not going to get a high end system. I have a BFG 640Mb 8800GTS, and it is great, I would recommend that.