Don't even bother, unless you're willing to buy a new motherboard.
Just because the Pentium D processor in your computer is LGA 775, that doesn't mean the Core 2 Duo will work in your motherboard. I had a Dell that was compatible with an LGA 775 Pentium 4 and Pentium D, but I installed a Core 2 Duo processor into it and it wouldn't boot up, killed the BIOS actually.