We present simulations of spheres with a rough surface in two-dimensional (2D) vibrating boxes. We introduce a collision model based on recent experiments with colliding sprees. During the collision of two rough particles, energy is dissipated and, possibly, linear momentum is transferred to rotational momentum. We examine the model system by varying the parameters as, for example the coefficient of friction μ. Using an event driven algorithm, we focus on the fluidized regime, i.e., on the case of rather small densities. We find that the behavior of the system depends on the frictional properties of both particles and walls. Introducing the particle-particle friction changes the behavior quantitatively. Rough, dissipative walls lead to a qualitative change of the system's behavior in the case of low densities. We present an expression for the ratio of kinetic and rotational energy in terms of the particle's moment of inertia, of the coefficient of friction, and of the tangential restitution. Furthermore, we compare our simulations with recent experiments on vibrated granular systems in 2D.