Recovering Git repository from objects only

I have a Windows box which has taken it into it's head to delete most of a Git repository (must have tripped the Important Work Detector ;). All I have left (that I can find) is the objects. I'm not sure how complete the collection of objects is, either. Is it possible to recover things from just the objects? As far as I can tell, the object tree is intact. All the packs and loose objects are in place; I just don't have the metadata to convince Git.