Neanderthal's cranial capacity was larger than ours, they had tools, art, cared for their sick and injured, and buried their dead. Just because they didn't know as much as we do now doesn't mean they were unintelligent.
With that out of the way, it's entirely possible there was no concept of an afterlife, god(s), or even ghosts during prehistoric man's reign on earth. If their idea of a full and complete life was to live long enough to bring their own offspring into the world why would they have "unfinished business" when they passed? Of course, I'm in no way insinuating that's the only reason for a spirit to stick around after death.
Another possibility for a pronounced lack of prehistoric ghosts could simply be too much time has passed. Neanderthals were around for 250k years, we've been here for around 100k years. Various minerals and elements are fantastically amazing when it comes to holding on to energy. How long can they do that for, though? If we managed to run a current through a quartz crystal embedded with just one single word, how long would it "last"? I don't know the answer to that, but I'm guessing centuries is definitely within the realm of possibility. A few thousand years? Maybe. A few thousand decades? I'd be inclined to say no to that one, any battery can holds its charge for only so long before it dissipates over time.
Ordania, theories are like questions, there aren't any stupid ones and they all hopefully lead to gaining more knowledge, and they certainly can't get you into trouble! Well, as long as you don't get sent back in time to the nearly four century period of horror known as the Spanish Inquisition!