We prove a process-level large deviation principle for quenched random walk in random environment subject to a random potential. In particular, both quenched random walk in random environment and quenched polymers in a random potential are covered. The walk lives on a square lattice of arbitrary dimension and has an arbitrary finite set of admissible steps. The restriction needed is on the moment of the logarithm of the transition probability and the potential, in relation to the degree of mixing of the ergodic environment. The rate function is an entropy and two variational formulas are given for the free energy.