We report on the observations of gamma-ray burst (GRB) 190114C by the Fermi Gamma-ray Space Telescope and the Neil Gehrels Swift Observatory. The early-time observations reveal multiple emission components that evolve independently, with a delayed power-law component that exhibits significant spectral attenuation above 40 MeV in the first few seconds of the burst. This power-law component transitions to a harder spectrum that is consistent with the afterglow emission observed at later times. This afterglow component is clearly identifiable in the GBM and BAT light curves as a slowly fading emission component on which the rest of the prompt emission is superimposed. As a result, we are able to constrain the transition from internal shock to external shock dominated emission. We find that the temporal and spectral evolution of the broadband afterglow emission can be well modeled as synchrotron emission from a forward shock propagating into a wind-like circumstellar environment and find that high-energy photons observed by Fermi LAT are in tension with the theoretical maximum energy that can be achieved through synchrotron emission from a shock. These violations of the maximum synchrotron energy are further compounded by the detection of very high energy (VHE) emission above 300 GeV by MAGIC concurrent with our observations. We conclude that the observations of VHE photons from GRB 190114C necessitates either an additional emission mechanism at very high energies that is hidden in the synchrotron component in the LAT energy range, an acceleration mechanism that imparts energy to the particles at a rate that is faster than the electron synchrotron energy loss rate, or revisions of the fundamental assumptions used in estimating the maximum photon energy attainable through the synchrotron process.Read less <