We investigate the conformation aid relaxation dynamics of single DNA molecules in strong confinement (smaller than persistence length) with coarse-grained semiflexible chain (SFC) models using overdamped Langevin dynamics simulations. DNA properties in nanochannels and nanoslits are studied in confinement with height (H) ranging from the DNA radius of gyration (R-g) to smaller than the persistence length (P). Qualitatively different dependences of chain conformation and relaxation time on H in moderate (P < H < R-g) and strong (H < P) confinement are observed for very stiff SFC in the nanochannel but not in the nanoslit. The chain relaxation time (t(relax)) exhibits strong power-law dependence in H < P nanochannels, verified with and without including hydrodynamic interactions (HI). The inclusion of hydrodynamic interactions affects chain relaxation dynamics even in strong confinement, indicating the intersegmental hydrodynamic interactions affect dominant segmental relaxation mechanisms of strongly confined polymers.