We present a detailed analysis of the composition and nucleosynthetic origins of the heavy elements in the metal-poor ([Fe/H]=-1.62+/-0.09) star HD 94028. Previous studies revealed that this star is mildly enhanced in elements produced by the slow neutron-capture process (s process; e.g., [Pb/Fe]=+0.79+/-0.32) and rapid neutron-capture process (r process; e.g., [Eu/Fe]=+0.22+/-0.12), including unusually large molybdenum ([Mo/Fe]= +0.97+/-0.16) and ruthenium ([Ru/Fe]=+0.69+/-0.17) enhancements. However, this star is not enhanced in carbon ([C/Fe]=-0.06+/-0.19). We analyze an archival near-ultraviolet spectrum of HD 94028, collected using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope, and other archival optical spectra collected from ground-based telescopes. We report abundances or upper limits derived from 64 species of 56 elements. We compare these observations with s-process yields from low-metallicity AGB evolution and nucleosynthesis models. No combination of s- and r-process patterns can adequately reproduce the observed abundances, including the super-solar [As/Ge] ratio (+0.99+/-0.23) and the enhanced [Mo/Fe] and [Ru/Fe] ratios. We can fit these features when including an additional contribution from the intermediate neutron-capture process (i process), which perhaps operated through the ingestion of H in He-burning convective regions in massive stars, super-AGB stars, or low-mass AGB stars. Currently, only the i process appears capable of consistently producing the super-solar [As/Ge] ratios and ratios among neighboring heavy elements found in HD 94028. Other metal-poor stars also show enhanced [As/Ge] ratios, hinting that operation of the i process may have been common in the early Galaxy.