So today, I decided to fiddle with my once bunk laptop. 2 hours of formatting and recovery later, my laptop is as good as new

. now that it's back from the dead, I wanna do some upgrades with it; maybe replace the HDD with a small SSD, upgrade the OS on it, and possibly upgrade the CPU on it. This brings me to my question.
My current CPU is a Intel C2D T5750. I was wondering if I am able to upgrade this to either a C2D P8400 or P8600. They are all the same socket type (Socket P), but they use a different manufacturing process. I am also unsure if the new CPU will be incompatiable with the chipset on my laptop's mobo.
Specs of my current Laptop:
Gateway Support - M-6874h Notebook Specifications
Current CPU:
Intel® Core
C2D P8400:
Intel® Core
c2d P8600:
Intel® Core
So can I make the upgrade?