1. A dog must either be confined or under supervision (that would have prevented the dog from going to the neighbor's place) -- and if the neighbor did poison the dog, it would have prevented that too.
2. When a dog was that sick, why wasn't it taken to the Vet?
I hate to say it this way -- but there is no other way -- the dog's death was your fault.
I agree with terbzz and Doc, You should of at least taken him to the vet!
I can't guess whether your nieghbor poisoned your dog or not. I had a friend who's dog got into rasins last year. The same kind of signs were present so he took him to the vet and after 4 days and 3 nights staying there they had to put him down. The only real way of knowing is by going to the vet.