By analyzing, on a picoseconds time scale, the fluorescence decay of a donor undergoing Förster resonance energy transfer in a suitable donor-acceptor system we can reveal DNA sequences that are specific of genetically correlated diseases. Since we use picosecond excitation from a continuous-wave mode-locked laser and time-correlated single-photon detection, we achieve such a high acquisition rate, sensitivity, and temporal resolution that we can perform the measurements on the human genomic DNA contained in cells that were simply lysed. We show that, in few minutes, we identify an individual, even heterozygote, carrying the sequences of the DQB1 gene that confers susceptibility to the development of insulin-dependent diabetes mellitus with no need of DNA extraction, purification, PCR amplification.