Just curious to see if this is possible......
 
My DAW is running on my Laptop with no firewire capabilities, no expansion slot.
 
Is it possible to add a firewire pci card to another computer tower and network the two together and then be able to run a piece of firewire hardware such as a Presonus Studio live mixer with my DAW? 

nope at least not with any acceptable type latency nor would it make sense if you have a desktop why use the laptop

I've tried Firewire cards on a laptop, several including the "desired" T.I. chipset.  I had an Alesis IO 26 and it connected but had dropout problems.  I tried it with a Focusrite Saffire Pro 40 and had a temporary Firewire port hardware failure in the Saffire Pro 40.  (The Saffire Pro 40 has two Firewire ports, and one did not work for several months after trying it with the T.I. chipset card in a laptop.  Not sure how it "fixed itself" but eventually starting working again).
 
The Saffire Pro 40 finally died (the estimate to repair it was within $50 of what I paid for it) and I replaced it with a USB connected unit and no more port compatibility issues and even lower latency with the USB units.

   "nor would it make sense if you have a desktop why use the laptop"   Because as I said.....My DAW is running on my laptop. The desktop tower would be a slave for the firewire pci card.  Just asking if it were possible. Thanks

 
 
 
Edit: I kind of doubt it will be fast enough connection to be useable, but it would be a fun experiment. Have you considered a crossover cable to hook the PCs up?
 
Edit 2: What do you plan on hosting, the audio driver? I don't know but
 

I'm just exploring options to incorporate firewire capabilities without having to buy a new computer. I was foolish at the time of my computer build not knowing what FireWire was used to do. Maybe sometime soon someone will make a usb mixing board that will work with a DAW like FiWi. They keep saying firewire is fading away....