It has also been suggested that the detection of a wealth of very low amplitude modes in Delta 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, a space mission developed and operated by CNES. This work presents the results obtained on HD 50844: the 140,016 datapoints were analysed using independent approaches and several checks performed. A level of 10^{-5} mag was reached in the amplitude spectra of the CoRoT timeseries. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0--30 d^{-1}. All the cross--checks confirmed this new result. The initial guess that Delta Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high--degree modes (up to ell=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. Probably due to this unfavourable evolutionary status, no clear regular distribution is observed in the frequency set. The predominant term (f_1=6.92 d^{-1}) has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data. This work is also based on observations made with ESO telescopes under the ESO Large Programme LP178.D-0361 and on data collected at the Observatorio de Sierra Nevada, at the Observatorio Astronomico Nacional San Pedro Martir, and at the Piszkesteto Mountain Station of Konkoly Observatory.