I don't think you can swap CPUs - C2D is Socket 755, while i7-3xxx is 1155. I've seen some people putting Xeons here, with small socket mod.
Whether you can change the motherboards - check your existing motherboard and its connection to the case. Many Dell desktops have proprietary front-panel connectors, which makes motherboard swap difficult.
And last but not least - that Dell (and its PSU) are at least ten years old. If you want new motherboard, you'll want also new GPU, hence new PSU.
Edit: F'uget about it - this is BTX motherboard and case. See Page 18
https://downloads.dell.com/manuals/...ion/precision-t3400_reference guide_en-us.pdf