The current gold standard gaming CPU is about 3x what your current CPU is. It is called an i5-2500k and it costs about $220.
A reasonable budget video card is a HD 6850 that costs about $150. It will give about 3x the FPS of an 8800 GTS for graphics intensive things. This card will get you medium or high settings for most games on good monitors without having to choose the lowest possible resolutions. It isn't ideal for a "real" gamer, but it is ideal for those who want the best bang for their (low) bucks.
The hard drive and the OS can stay if you get a new build from scratch. If that happens, a "standard" gamer build would run you maybe $600 - $700 for the rest of the parts.
If you are prepared to shell out that sort of money, I can spec you out some parts that you can just click on the links and order from Newegg.
If you aren't prepared to go that route, I am not real sure how far you can take the current system.
If you get a new video card, a lot of its capability you likely won't be able to utilize, because it will be held back by the weak processor. New video cards are commonly hindered in their performance when they are added to older processors in this way.
There is some middle ground here too, if you are only interested in shelling out maybe 400 - 500 then you can probably get medium or high settings on most games, but not able to max or get 90% of the way on most anything.
I am sure there are some people who would be interested in helping you spec out things that you can add to the current system to keep it going a little bit longer, but I am not so interested in doing so because I don't think you will have a good experience going this route.