That is a basic use system made with basically a laptop motherboard with a soldered CPU and laptop RAM. You can't even move the CPU and RAM to another system which would have been an option with a more standard desktop PC. You are better off spending $100-150 to get a better tower system with a 16x slot and a 300watt power supply instead of trying to get a cheap card into a cheap computer for gaming. Two piles of junk is not better than one pile of something decent.
So I also ended up ordering a new HP 300 watt power supply ($55) that the HP 3400 MT requires and a new 2 GB Ati Radeon HD 7570 PCIe x 16 graphics card ($87.00) that I found online.
Total Spent: $55 + 55+ 87 = $197.00
Edit... the link went to an ended item.I think I found a replacement for the motherboard. Now I am asking if it has a full PCI express slot.
I have a total of 6 spots for screws, and this motherboard looks better.