The dynamics of low molecular weight polybutadiene (PB) functionalized with side chains able to form hydrogen-bonded networks is investigated by a combination of calorimetry, rheology, and broadband dielectric spectroscopy (BDS). The modified PBs are found to have extremely different macroscopic viscosities with respect to the starting polymer; however, rather unexpectedly, when investigated using these three techniques, we find that the changes to the segmental motion responsible for the glass transition temperature remain unchanged. This is attributed to the high flexibility of the side chain, which does not restrict the motions of the highly flexible segments in the PB chain. In the presence of the hydrogen-bonded network we observe in both the rheological and dielectric spectra an additional relaxation, orders of magnitude slower than the segmental relaxation. We find that the temperature dependence and its dynamics are well explained in terms of the lifetime of the hydrogen bond, with a binding energy of about 100 kJ/mol.