Emission linewidths of quantum dot photonic-crystal-slab nanocavities are measured as a function of temperature and fabrication parameters with low-power and high-power, cw and pulsed, nonresonant excitation. The cavity linewidth is dominated by the absorption of the ensemble of quantum dots having a density of ~=400/µm2; above the absorption edge, the cavity linewidth broadens considerably compared with the empty cavity linewidth. Gain and lasing are seen for high-power pumping; it is estimated that only a small number of quantum dots contributes to the lasing.