If you are going to build a new "system" around the 560ti and use all new parts
I would pick these (in keeping the same mid-tower config of the dell):
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119233 = $60.00
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131781 = $120.00
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115072 = $220.00
Others will have a different point of view.
Now the above will give you a new case, motherboard and CPU. If I had to replace all those items in your "build" they would be what I'd chose.Without knowing what you intend to keep out of the Dell, that's all that I can recommend at this point.
If we knew:
What ram is in the Dell?
What PSU?
Can the mobo and cpu from the Dell be reused?
What is the cpu?
What are the spec's of the mobo?(I'm sure it's proprietary so a model # probably won't help us)
With these answers we could give better advice.
Maybe the Dell's "better power supply" won't meet the minimum req's of the 560ti and it will have to be bought?
I'm pretty sure the Dell uses DDR3 which is good - but what speed is it?
If it's at least 1333 it could be used in your new system.
Sorry to lay all this on you but you
have to consider it all.