It appears your Dell uses a Core 2 series Intel processor. That is a different socket than the i7, so no, you can not use that processor.
To do so, you would need a new motherboard (and a new OS), and memory(DDR2 to DDR3)
I would simply get a new machine. I know that's not alwasy possible, but if you want to build or upgrade your machine you should start on a newer platform.