Today, most new video cards would use PCIe or PCI Express slot and they are normally $20 cheaper than an AGP video card. AGP slot is getting old and companies would not anymore make AGP video card.
Like Ovrclkr said, your motherboard is an AGP motherboard because it is old and does not have a PCIe slot. You need a new PCIe motherboard if you wanna buy newest, better PCIe video card.
Your old system is actually limiting your upgrade path and you cannot even go with the newest DirectX 11 video card. Your old CPU's speed would also bottleneck the new video card's speed and 1GB of DDR does not even meet minimum requirement for the latest video card.
I hate to say this but seriously, you better build a new PC rig and get the new system before even considering spending money on buying new video card. Also, you don't wanna miss DirectX 11 quality graphic games because DX 11 would offer more realistic graphics for your games so if you have a newer system, you could have gone with at least something like Radeon HD 5770 or Radeon HD 5850 and being able to get a better gaming experience.
Actually, I am selling my 2004 Pentium 4 Sony Vaio Desktop PC and I am currently building a new Core i5 PC for gaming.