The white dwarfs are promising laboratories for the study of cosmochronology and stellar evolution. Through observations of the pulsating white dwarfs, we can measure their internal structures and compositions, critical to understanding post-main-sequence evolution, along with their cooling rates, which will allow us to calibrate their ages directly. The most important set of white dwarf variables to measure are the oldest of the pulsators, the cool DA variables (DAVs), which have not been explored previously through asteroseismology due to their complexity and instability. Through a time-series photometry data set spanning 10 yr, we explore the pulsation spectrum of the cool DAV, G29-38 and find an underlying structure of 19 (not including multiplet components) normal-mode, probably l=1 pulsations amidst an abundance of time variability and linear combination modes. Modeling results are incomplete, but we suggest possible starting directions and discuss probable values for the stellar mass and hydrogen layer size. For the first time, we have made sense out of the complicated power spectra of a large-amplitude DA pulsator. We have shown that its seemingly erratic set of observed frequencies can be understood in terms of a recurring set of normal-mode pulsations and their linear combinations. With this result, we have opened the interior secrets of the DAVs to future asteroseismological modeling, thereby joining the rest of the known white dwarf pulsators.