I wish I could help you on the power supply part, but the fact of the matter is that its an OEM (original equipment from manufacturer) supply designed specifically to fit in that box. You're not going to be able to shoehorn/shove a power supply in there unless you have the technical know-how to actually take it apart and put it into the current power supply container that you have.
Like bsphil said, the 220 I previously mentioned will run FFXIV, not at a glorious 60fps, but it will at least render it, with your current power supply to boot.
As for your PCI 1X ethernet card, you can always remove that and go with a USB ethernet solution (roughly 30 bucks) or wireless if you have it.
Your unequivocally best option is to seriously look at what you have in removable parts
-E5200 Dual core processor (2.5ghz)
-4 Gigs of DDR2
And start drafting a plan to get a beefier model. There are a literal TON of options for a 775 socket processor using DDR2 memory if you wish to stick with that. Just roughly ballparking it...
Processor - free
RAM - free
Motherboard - 35 bucks http://www.newegg.com/Product/Product.aspx?Item=N82E16813153157
Case - 40 (See previous post)
Power Supply - 70 (Assuming you want to keep that MONSTER of a video card)
That is just a suggestion though
In reality you would be better off starting off with a decent base, there is a combo sale right now at NewEgg, I'll list all three, but I think this
one would be the most bang for your buck since you already have the graphics card, but it'll send you out of budget obviously. Slightly older tech, but comes with ATI card Mid-Range, but very expandable Their 'gaming' combo, no graphics card included