We use photon correlation measurements to study blinking in single, epitaxially grown self-assembled InAs quantum dots situated in circular Bragg grating and microdisk cavities. The normalized second-order correlation function g((2))(tau) is studied across 11 orders of magnitude in time, and shows signatures of blinking over time scales ranging from tens of nanoseconds to tens of milliseconds. The g((2))(t) data is fit to a multilevel system rate equation model that includes multiple nonradiating (dark) states, from which radiative quantum yields significantly less than 1 are obtained. This behavior is observed even in situations for which a direct histogramming analysis of the emission time-trace data produces inconclusive results.