Most of the DNA sequenced from the Neanderthal genome projects came from the microbes that decomposed the dead fella'. This poses a problem for the human geneticists who are only interested in the Neanderthal DNA. But you could probably do some interesting things with the non-Neanderthal DNA. John Hawks says:
I suppose if you were interested in the long-term microbial decomposition of fossil bone, you could do your dissertation on those. For the rest of us, the final step is to let the computer spit out the humanlike sequences, which are assumed to be the Neandertal DNA plus some proportion of human contamination.
Do these sequences fall under the Bermuda agreement? If so, I agree with John -- this could be an awesome project!