Your computer's hardware appears to be incapable of running Mountain Lion. To tell for certain, choose About this Mac from the Apple menu, click on More Info, and check the model identifier against the following:
A computer incapable of running Mountain Lion which has a Core 2 Duo(not Core Duo) or better CPU and at least 2GB of RAM can run Lion 10.7, which is available by phoning the online Apple Store and ordering a download code for it.
System requirements for OS X Lion and Mac OS X v10.6
Learn the system requirements for OS X Lion and Mac OS X v10.6.
OS X Lion system requirements
To use Lion, make sure your computer has the following: