We present the results of molecular dynamics simulations of SPC/E water confined in a realistic model of a silica pore. The single-particle dynamics have been studied at ambient temperature for different hydration levels. The confinement near the hydrophilic surface makes the dynamic behaviour of the liquid strongly dependent on the hydration level. Upon decrease of the number of water molecules in the pore we observe the onset of a slow dynamics due to the "cage effect''. The conventional picture of a stochastic single-particle diffusion process thus loses its validity.