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Check fuses #41 & #35 in the fuse box under the dash if they are good, the ACC Delay relay in the instrument cluster may have been damaged. In that case the cluster will have to be replaced.
If fuses 41 and 35 are ok then the instrument cluster is defective, as the power windows are fed through the battery saver relay and the under hood lamp is fed by the interior lamp relay which are both internal to the instrument cluster and not serviceable without replacing the cluster.
Yes, because all the battery saver relay controls are interior lites and acc, and the exterior lites if they are left on for and extended period with the engine off.