We have carried out an in-depth study of the peripheral region of the molecular cloud L1204/S140, where the far-ultraviolet radiation and the density are relatively low. Our observations test theories of photon-dominated regions (PDRs) in a regime that has been little explored. Knowledge of such regions will also help to test theories of photoionization-regulated star formation. [C II] 158 mum and [O I] 63 mum lines are detected by the Infrared Space Observatory at all 16 positions along a one-dimensional cut in right ascension. Emission from H-2 rotational transitions J = 2 --> 0 and J = 3 --> 1 at 28 and 17 mum, respectively, was also detected at several positions. The [C II], [O IO], and H-2 intensities along the cut show much less spatial variation than do the rotational lines of (CO)-C-12 and other CO isotopes. The average [C II] and [ O I] intensities and their ratio are consistent with models of PDRs with low values of far-ultraviolet radiation (G(0)) and density. The best-fitting model has G(0) similar to 15 and density n similar to10(3) cm(-3). Standard PDR models underpredict the intensity in the H-2 rotational lines by up to an order of magnitude. This problem has also been seen in bright PDRs and attributed to factors, such as geometry and gas-grain drift, that should be much less important in the regime studied here. The fact that we see the same problem in our data suggests that more fundamental solutions, such as higher H2 formation rates, are needed. Also, in this regime of low density and small line width, the [ O I] line is sensitive to the radiative transfer and geometry. Using the ionization structure of the models, a quantitative analysis of timescales for ambipolar diffusion in the peripheral regions of the S140 cloud is consistent with a theory of photoionization-regulated star formation. Observations of [C II] in other galaxies differ from both those of high-G(0) PDRs in our galaxy and the low-G(0) regions we have studied. The extragalactic results are not easily reproduced with mixtures of high- and low-G(0) regions.