We consider a quasistatic frictional contact problem with a subdifferential boundary condition for general thermo-electro-elastic-viscoplastic materials. The frictional contact is modeled by a general velocity-dependent dissipation function. We derive a weak formulation of the system and then prove the existence of a unique weak solution to the problem. The proof is based on arguments of evolutionary variational inequalities, parabolic equations, the variational equation, differential equations, and the fixed-point theorem. Finally, we describe a number of concrete contact and friction conditions to which our results apply.