5670 is a great card. Toyota and Happy Medium are great resources here, even if Toyota is a bit pessimistic with CPU power (I am too, TBH). Still, a 5670 plugged into your current box will be full of win, particularly if you go easy on settings a little bit. In my experience the easiest things to turn down that don't make all that much difference at your native res (1680x1050) are AA and Shadows. High shadows can murder some games and don't really add that much imho.
Next upgrade should be PSU. Keep your original one.
From there, save up and you should be able to buy all of this at the same time :
SB mobo
Low end SB
or
8x0 mobo
PhII X6 / BD
and
4-8GB DDR3
1TB Sata NCQ WD Black
Basic Case
DVDRW+BDReader
Accessories
Should be fairly cheapish to do, perhaps shoot for next spring/summer.
After doing that you may be able to pick up something like 6850 or whatever else is a good value ~$150ish card at that time. Reload your old Dell box with original video and PSU and sell it for $whatever.
Happy gaming!