You might be able to remove the dents with steam. Soak a towel in warm water, and using an iron (the kind you use on clothing) on its hottest setting, briefly touch a dent with the iron/towel so as to apply steam to the dented area. Like a sponge, wood is porous, and when it gets dented, the pores are compressed. Steam opens the pores back up and lifts the dents. Chips and gouges are a different story, because in those cases, wood is actually removed and cannot simply be "reinflated."
You should sand the neck down to bare wood before you do it for best results. Experiment with scrap wood before you touch the neck, though; the wood can start to burn if the iron is on it for too long.