No this will not work in your typical atx case. On your pic of your pc ... the vid card and sound (which both appear to be onboard) are all spread out horizontally.
If you look at a pic of a newer motherboard ... all the connections ... i.e. ps/2, usb, audio, ethernet LAN ... are all within a 2"x6" area. Look at this for an example: http://www.newegg.com/Product/Showim...board+-+Retail
See the difference? Look at this ATX case: http://www.newegg.com/Product/ShowIm...y%20-%20Retail
Your connections need to fit in that area. Your motherboard will come with a custom faceplate to match its own connections ... you would knock out the faceplate that comes with the case and use the motherboard one.
Does this clear it up more for you?
***edit*** BTW ... it looks like your original motherboard uses a riser board system for it's PCI connections (connects perpendicular to the motherboard) ... thats what all those silver slots above your video and audio connections are. Those would be the slots for your ethernet LAN card if you wanted to install one. I'd just leave that pc alone ... possibly paint it ... maybe use some chrome spray paint and create a cool look. Of course ... remove the stuff inside first so you dont mess any of it up.