The languages in contact theory sounds interesting, but if you go across the English Channel you find that the same thing happened across the board with the transition of Latin into Romance languages. (Latin's cases were probably falling together (phonoloigcally) in the Republic, and were still being written well past the fall in the west.) Another problem I have with this, is that we don't see the non-contact dialects preserving more cases than the contact variety. Since OE got interrupted (by William) during its attempted standardization (by Alfred's West Saxon court) by the introduction of the Norman variety of French, I guess we'll never know.
But, there is a theory of language change called accomodation theory (via Peter Trudgill) that says when two different language-speaking groups are trying to actually communicate, they accomodate their language towards each other, and that this accounts for some change. There's no doubt that the Vikings in the Danelaw affected English, but I think it's mainly in vocabulary (she and they are borrowed from the Norse) and not in case abandonment.
Anyway, just my tuppence. Cum grano salis. &c.
