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Using fluorescence microscopy and single-particle tracking, we have directly observed the dynamics of λ-DNA trapped inside poly(acrylamide-co-acrylate) hydrogels under an externally applied electric field. Congruent with the recent discovery of the nondiffusive topologically frustrated dynamical state (TFDS) that emerges at intermediate confinements between the traditional entropic barrier and reptation regimes, we observe the immobility of λ-DNA in the absence of an electric field. The electrophoretic mobility of the molecule is triggered upon application of an electric field with strength above a threshold value Ec. The existence of the threshold value to elicit mobility is attributed to a large entropic barrier, arising from many entropic traps acting simultaneously on a single molecule. Using the measured Ec which depends on the extent of confinement, we have determined the net entropic barrier of up to 130 kBT, which is responsible for the long-lived metastable TFDS. The net entropic barrier from multiple entropic traps is nonmonotonic with the extent of confinement and tends to vanish at the boundaries of the TFDS with the single-entropic barrier regime at lower confinements and the reptation regime at higher confinements. We present an estimate of the mesh size of the hydrogel that switches off the nondiffusive TFDS and releases chin diffusion in the heavily entangled state.