The turn-on-time statistics for an individual longitudinal mode and the total intensity of a multimode laser are shown to be very different. In both experiment and theory we find that the differences are due mainly to transitory modes that decay as a result of frequency-dependent losses and gains. Associated with this phenomenon is a kink in the time evolution of the mode intensity, but not in the total intensity, that represents a transition in the dynamics from domination by independent growth of all modes to domination by competition between modes with different net gains. This unequal competition increases the average and the standard deviation of the individual mode turn-on time. The experimental dye-laser system has a thin gain medium (100 m) that is strongly coupled to a short cavity (2.5 cm) and is adjacent to one of the cavity mirrors. The opposite cavity mirror serves as a relatively weak output coupler. The presence of the thin gain medium in the cavity causes the effective pump and loss rates to be frequency dependent. The result is a transient spectrum in which the cavity modes that have the highest net gain dominate the system more as the turn-on transient progresses. The gain spectrum is found to be strongly affected by the frequency dependence of the compound-cavity modes. Using realistic laser parameters, numerical simulations of a multimode laser model ͕developed in companion paper [J. Opt. Soc. Am. B 14, 191 (1997)]͖ yield turn-on dynamics and statistics that agree well with those measured experimentally.