Thanks for the pic, as Richards says above, that is a PCI-E slot (the longer one above the wireless card).
That photo actually also shows the model number of the motherboard (it is an MSI Ms-7309 Ver 1.0).
I had a look at the specs and that has a PCI-E x1 slot (the short one at the top), a PCI-E x16 (the long one and the one that is of interest) and two normal PCI slots (you have your wifi card in one of them).
There are two profiles of card - full height (which is what you want) or half height/low profile (generally these are for smaller cases and the circuit board tends to be smaller and the bracket that you fix it in with, shorter.
The quadro card Richard has linked to should work fine (you will likely need to download drivers, from the NVidea website)
One of these will also do the job:
http://www.ebay.co.uk/itm/ATI-Radeon...item5d4313c2f7
Once you have installed the card and drivers, you will need to go into your display properties and configure the dual screens (the extend my monitor onto this screen tick box).