Well, the card I was prescribing in my signature uses what is known as AGPx8, or AGP8x, more commonly. The multiple relating to speed and capacity of the video card. In any case, you have an AGP port. Your port says specifically no AGPx2 (old as hell), which works at more than double the voltage of the GeForce 7800GS, a card that uses 1.4/1.5volts.
I also ask how old this machine is, as the voltage is okay, but the GeForce 7800GS requires a bit of system power. Your power supply, usually a big grey box above the processor (lots of power cords out of its back) controls this factor. The card stats say you need a 350watt power supply. So on the inside of your case, check the stickers on the box and see what info you can dig up. Even so, if you're getting the card, I wouldn't touch it without a 450 watt.
The problem is, I don't know what you're using as far as computer builds. If you can supply me with a model name and company, I could find out alot about what your system could do with this situation.