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The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1 B u (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans' correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S 1 (2 1 A g ) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 1 1 B u and 2 1 A g states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S 2 (1 1 B u ) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1 B u surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.