A simplified theory of enhanced ultraviolet, visible, and infrared photochemistry near rough dielectric and metallic surfaces is described and numerically investigated. Protrusions on a rough surface are modeled as isolated microscopic spheres. We formulate classical equations of motion for molecules interacting with electromagnetic fields and such material spheres. The model incorporates (a) dipole-dipole coupling between absorbing molecules and the large, induced dipoles created in microscopic spheres irradiated near Mie resonances, and (b) dissipative energy transfer from excited molecules to higher order (l>1) multipole resonances in the spheres. Calculations show that substantial enhancements in photochemical yields are possible for relatively slow chemical reactions as well as fast reactions. The similarities and differences between enhanced photochemistry and surface enhanced Raman scattering (SERS) are discussed in detail. Dielectric materials for enhanced infrared photochemistry at CO2 laser wavelengths are proposed.