We present a compact model of transport through a random distribution of interacting quantum dots embedded in a dielectric matrix. The model is based on a network of interconnected tunnel junctions sandwiched between two electrodes, resulting in a system of nonlinear differential equations which is numerically solved for a given time-dependent voltage applied to the gate. The capacitance matrix, electron/hole tunneling currents and the effective area of conduction between quantum dots are calculated at each integration step. The transport properties obtained from the model are successfully validated against experimental data for a silicon nanocrystal basic MOS cell, showing its potential applicability to non-volatile memories. In addition, through a simple rate equation, the calculated charge flux tunneling or impacting the nanocrystals is converted into electroluminescence. In this regard, we discuss the origin of the recently reported field effect luminescence in silicon nanocrystals. It is found that the idea of quantum-confined exciton creation through sequential injection of opposite sign carriers is in contradiction with the model and with the electron/hole tunneling time ratio obtained through the WKB approximation due to the difference in the electron and hole potential barrier heights. We show how our model of transport, along with a rate equation with the reported value for the absorption cross section for electrical excitation of silicon nanocrystals (~10⁻¹⁴ cm²), is in good agreement with experimental data obtained under pulsed excitation, without requiring further assumptions such as the formation of excitons from hole tunneling into electron-charged nanocrystals, revealing impact excitation of electrons/holes from the same substrate as the physical origin of the observed field effect luminescence.