It has been suggested that the detection of a wealth of very low amplitude modes in δ Sct stars was only a matter of signal-to-noise ratio. Access to this treasure, impossible from the ground, is one of the scientific aims of the space mission CoRoT, developed and operated by CNES. This work presents the results obtained on HD 50844: the 140,016 datapoints allowed us to reach the level of 10-5 mag in the amplitude spectra. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0-30 d-1. The initial guess that δ Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high-degree modes (up to = 14) are identified. We also prove that cancellation effects are not sufficient in removing the flux variations associated to these modes at the noise level of the CoRoT measurements. The ground-based observations indicate that HD 50844 is an evolved star that is slightly underabundant in heavy elements, located on the Terminal Age Main Sequence. The predominant term (f1 = 6.92 d-1) has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data.