I have the G61-631 which has the same CPU and the 785GX chipset. My socket is S1 (S1G3 to be specific). The Phenom IIs are S1G4 (Gen 4), however a quick search on AMD's website shows the 785G should support it. HOWEVER, All of the Phenom II's I have seen are DDR3, and the M300 is DDR2. Since AMD has the memory controller on the chip, and the socket is different for DDR3, I am thinking it would be incompatible.
The best processor I have found for S1G3 is the AMD Turion II M660 2.7ghz
Here you can see the Phenom II N930 is DDR3:
I'm not sure if the memory controller is backwards compatible.