Well, the Model # 0968h seems to point to the HP Desktop dc7100. The problem is, there are three versions of that system:
1) Ultra-Slim - Has one available full height PCI slot
2) Small Form Factor - Has one available low-profile PCI-Ex16 slot
3) Convertible Mini-Tower - Has one available full height PCI-Ex16 slot
The question is, which do you have?
Take a look at these system images
and see if you can tell us which one (if any) you have.