Non-equilibrium and equilibrium adiabatic mixed quantum-classical molecular dynamics computer simulations of the solvation dynamics of an excess electron in methanol are reported. We develop the connection between the multiple time scales reflected in solvent response and individual physical phenomena, such as the radial collapse of the electron and structural relaxation of the hydrogen-bonding network of the solvent. The significant role of the latter aspect appears responsible for the breakdown of the linear response approximation for the relaxation of the adiabatic ground state energy of the excess electron.