Ya, you got it right there. Your old CPU can't feed that 5870. Personally, I'd look to see what's the best C2D your current mobo would support. If you can get a 45nm chip I would prolly go with one of those. Not sure how your feelings on OC'n are, but a 3Ghz or greater C2D would be the cheapest way to unlock (most of) the power of the 5870.
Sure a Core i5/i7/PII x4 setup would be great, but for $118 you can get an E7500 from NewEgg that'll get you most of the power from the 5870. That's way cheaper than replacing the mobo, CPU and RAM.