A discrete-to-continuum (DC) simulation approach is introduced to study the statics and dynamics of polymer chains in two dimensions with quenched barriers, a dirty surface. In our DC hybrid approach, the large-scale relaxation of polymer chains on a discrete disordered lattice is followed by off-lattice simulation using a bead-spring chain model with a finitely extensible nonlinear elastic (FENE) potential for covalent bonds and Lennard-Jones (LJ) potential for nonbonded interactions. Segregation/folding of chains, which occurs at low temperatures (T = 0.2, 1.0) with LJ interaction, becomes more difficult as the concentration of barriers increases, due to a screening effect of the barriers. In contrast to the chains' contraction at high temperature (i.e., T = 5) and their collapse in athermal systems, chains are elongated on increasing the barrier concentration-a barrier-induced stretching. Variations of the root-mean-square (rms) displacements of the center of mass (R-cm) of the chains and their center node (R-cn) with time (t) show power-law behaviors (R-cm similar to t(nu 1), R-cn similar to t(nu 2)) with nonuniversal exponents in the range nu(1) similar or equal to 0.40-0.05 and nu(2) similar or equal to 0.30-0.05, respectively, depending on temperature and barrier concentration. The radius of gyration (R-g) and the average bond length ([l]) expand on increasing the barrier concentration at low temperature and contract at high temperature, which is consistent with the variation of the width of the radial distribution function.