You should definitely go with a whole new build. You really don't have any upgrade choices without bottlenecking your PC. The things that you can upgrade won't be worth it because the price for performance is too high.
SATA is a connector, can you open your computer? If you can open your computer and do open it, do you see any wide cables? If you don't then chances are you are using a SATA connector.
There is also pictures here: http://en.wikipedia.org/wiki/Serial_ATA
We'll assume you have a SATA connector hard drive and that your budget is $500 (excluding OS):
Explanation: the i3 2100 is a great CPU, definitely great for gaming purposes. It performs top notch and can hyperthread into 4 threads, basically making a 2 core CPU into a 4 core CPU, which is great since it'll allow you to use this computer for a longer period of time. I chose the HD radeon 6870 because it is a great performing card. I have this video card and I can play BF3 at 1920x1080 on high perfectly fine. This card will give you great 1920x1080 graphics performance and outstanding 1680x1050 performance.
The motherboard is where you have a choice. You have to choose now. The lower price may look tempting, but I really recommend you go with the ASRock Extreme 3. The z68 chipset motherboard will allow you to upgrade to an overclockable i5 or i7 CPU in the future, it will also allow you to CrossFireX the HD 6870 when you have the money. The H61M-VS, however, cannot be upgraded (unless you take out the motherboard too) to an overclockable CPU (well you can, but you can't overclock with that board) or CF the graphics card. Next is the power supply. I gave you 2 options again, this is more based on your previous choice. Choose the OCZ if you go with the ASRock H61M-VS motherboard and go with the Antec earthwatts if you go with the Extreme 3 motherboard. You can go with the OCZ PSU with the Extreme 3 motherboard, but you'll need to upgrade the PSU if you're going to CF the graphics card. The Antec PSU would not require any upgrading if you wish to CF.
The NZXT Gamma is a great case, I would recommend it. It is a gaming case with room to support long graphics cards. I also have this case and the Radeon 6870 fits with some extra room. It will get somewhat cramped if you don't have a modular powersupply though...
8GB of RAM is more than enough for any gaming system. I haven't seen games use more than 3GB of RAM...and even if you allow the other programs another 1GB of RAM, you'll still have 4GB left over if you choose the 8GB RAM package.
You won't need an aftermarket Heatsink or Fan because you won't be overclocking (you can't) the i3 2100.
The DVD ROM is to install windows.