Gateway DX4300-11
Link above tells that you have a 300W power supply. Every graphics card will require a different amount of power. The power requirements I was suggesting will depend upon the graphics card you choose to purchase. Chances are very high that you will need a higher powered supply than 300W.
I'm also willing to bet that you don't have a six or eight pin power plug designed for the high power graphics with that power supply. This would also mean you would need to use the adapters that may or may not come with the card. However I would not recommend using the adapter. I'm not trying to confuse you, I'm simply bringing this necessary step to your attention.