What Firewire card do I install...or is it possible?

I would like to install a firewire card into my HP p6774y desktop. I bought a StarTech 4 port PCI 1394a Firewire card (I wrongly thought they were all the same standard size) and it does not seem to fit into the aprox. 3 inch slot. There are three other slots that are aprox. 1 inch long.

Should the firewire card I need have the short or long slot?

How do I know what slots I have and if I can even insert a firewire. I need help on this one!