Well that is the connector for the onboard video. The question is what slots the board has to add a real video card.
If you don't know what motherboard it is then CPU-Z can tell you on the mainboard tab; http://www.cpuid.com/softwares/cpu-z.html
Alright, your motherboard has an AGPx8 slot. Not as good as PCIE x16 but much better than only having PCI slots. What kind of processor do you have in there and how much ram? Any idea what PSU is in the system?
Alright, well, you can add a card but the problem is your processor is single core and not even a very fast one. Basically it isn't going to do well on current games. You can add a card but I think that CPU is going to struggle with WoW although it may be playable. There are few cards to pick from for AGP ports at this point and they are more expensive than they should be. This would be your best choice; http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Honestly you would be better off upgrading the system entirely rather than wasting money upgrading that thing. It really doesn't have to cost all that much to build a computer much, much better than what you have now. Just earlier I picked out some parts for someone else in a different thread so I'll just quote myself;
Well you can try the card see what happens but I don't think there should be much difference in performance. As for upgrading just the processor your motherboard really can't handle anything that would make it worth the cost and effort.