Liquid-gated silicon nanowire (NW) field effect transistors (FETs) are fabricated and their transport and dynamic properties are investigated experimentally and theoretically. Random telegraph signal (RTS) fluctuations were registered in the nanolength channel FETs and used for the experimental and theoretical analysis of transport properties. The drain current and the carrier interaction processes with a single trap are analyzed using a quantum-mechanical evaluation of carrier distribution in the channel and also a classical evaluation. Both approaches are applied to treat the experimental data and to define an appropriate solution for describing the drain current behavior influenced by single trap resulting in RTS fluctuations in the Si NW FETs. It is shown that quantization and tunneling effects explain the behavior of the electron capture time on the single trap. Based on the experimental data, parameters of the single trap were determined. The trap is located at a distance of about 2 nm from the interface Si/SiO2 and has a repulsive character. The theory of dynamic processes in liquid-gated Si NW FET put forward here is in good agreement with experimental observations of transport in the structures and highlights the importance of quantization in carrier distribution for analyzing dynamic processes in the nanostructures.