From what you have told me, it sounds to me like a lack of video processing power.  If you ar running in integrated Graphics card (built in to the motherboard), you will continue to have issues no matter how much ram you add to the system.  RAM is not going to be your solution.  What you need to do is a little research, or reply back to this and I will do it for you.  You need to find out if your computer is capable of accepting a PCI-Express or AGP video card. 

Computer gaming in todays world requires the use of a Video card for two reasons: 1. it takes the load off your processor. 2. It has its own memory.  Integrated graphics cards nad low end agp/PCI-e graphics cards don't have the power necissary to render extreme graphics.  Integrated, in particular has an issue because it is sharing memory from your system RAM, leaving you little ram to work with, as well as being short on the shared RAM.  WHere as a video card has its own processor to computer your graphics output, and its own memory to use.  However, the low end cards will not do the trick either when you get into a game like The Sims, because once you start putting more and more moving objectets on the screen, the video card has to work harder.

If you do not plan on playing anything extreme like Call of Duty 4 or AION, then a mid range card will work, and you are looking around 50-60 $ depending on the type of card you need.  If you can post your system information, like maybe a brand name and model i.e. Dell Dimension 9100.  Post your OS as well.  If its custom built, then I need to know the model of Motherboard you have and the maker.  i.e. ASUS A7N-X Ver 2.0.  With this info, I can make a suggestion on a card that will work for you.  You may get lucky and find a fitting card for under 40$, you just have to look in the right places:).