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We compute a one-component model of the solar atmosphere, including in that model the photosphere, chromosphere, and chromosphere-corona transition zone. The calculations are performed with PANDORA, a general computer program that enables us to obtain detailed solutions of the radiative-transfer and statistical-equilibrium equations for a six-level hydrogen atom and for eight-level C I and Si I atoms. All radiative transitions are treated explicitly. The program is formulated in a general way and is currently being used for the analysis of other atomic systems as well. The present calculation of the continuous absorption and emission throughout the spectrum takes into account the non-LTE contributions of H, H-, C I, and Si I. Other ions and atoms are treated in LTE. The atmosphere is assumed to be in hydrostatic equilibrium, but radiative equilibrium is not assumed. By trial-and-error adjustments, we obtained an empirical temperature-height distribution such that our computed synthetic intensities are consistent with the observed radiation from the chromosphere in the extreme-ultraviolet and microwave regions of the quiet solar spectrum. Our present determination of chromospheric structure differs from previous ones in that the Lyman lines are treated explicitly; they are not assumed to be in detailed balance. We find that small departures from detailed balance in the Lyman lines can lead to significant changes in the ionization of hydrogen in the middle chromosphere. The present paper is concerned mainly with the equations we solve in order to construct the solar model. Section XI gives a brief summary of the results. Further details will appear in subsequent papers of this series. Subject headings: atmospheres, solar - chromosphere, solar - spectra, solar