According to the dell site, your desktop has PCI-E, so you should be good.
http://www.dell.com/ca/p/studio-xps-8100/pd?cs=cadhs1
I would strongly urge you to consider the GTX570 instead. Unless you are running mutliple monitors or have 3D vision, you really don't need the GTX580. Even with Crysis 2 and battlefield 3, this card is an overkill.
GTX580 is for those freaks who have to have the latest tech at all times(who resell their gear every 6 months to get the latest stuff), or who are running multiple monitors with 3D vision... Besides the card will tank in price as soon as the GTX590 comes out. Look at what happened to the GTX480.







