A semiclassical model for studying charge transport in a two-dimensional molecular lattice is presented and applied to both a well ordered system and a system with disorder. The model includes both intra- and inter-molecular electron-lattice interactions and the focus of the studies is to describe the dynamics of a charge carrier in the system. In particular, we study the dynamics of the system in which the polaron solution is dynamically stable. It is found that the parameter space for which the polaron is moving through the system is quite restricted and that the polaron is immobile for large electron-phonon coupling and weak intermolecular electron interactions and dynamically unstable and disassociates into a delocalized electronic state decoupled from the lattice for small electron-phonon coupling and strong intermolecular electron interactions. Disorder further limits the parameter space in which the polaron is mobile.