Creating a menu page in a Object Oriented developed plugin

You have mix up in static and non-static usage. Your style is non-static, but your methods are declared as such. If you enable WP_DEBUG mode you’ll see following errors:

Notice: Undefined variable: this

Warning: call_user_func_array() expects parameter 1 to be a valid callback, first array member is not a valid class name or object

This happens because static method doesn’t “know” what $this refers to, since static isn’t tied to specific instance of the class.

Simply declare your methods as public rather than public static for this code organization.