Yes, that is my computer. Though I did buy it refurbished from here.
So would I be correct in assuming that I will need a replacement part to upgrade the psu? I haven't found anything about the psu in the specs. It is times like this when I realize just how little I know about computers.. I don't know what I would do without people like you guys. :D
EDIT: I looked around some more and found another card that I think will run fine with a 300w psu. I do not know if it is compatible further than that. It is an ASUS EAH6670/DIS/1GD5 - ASUS HD6670 graphics card with DirectX®11, HDMI, and Eyefinity support. More information can be found here