I'm actually having doubts about my earlier post. Of yours, only #2 is clearly correct. I'm honestly not sure if #1 would be considered correct, although it seems so to me.
#4 is not correct - Nor is a conjunction and shouldn't start a second sentence.
#3 might be the correct version of #1 - let's wait for someone else more well versed in the "neither" to comment. It strikes me as wrong, but I've been wrong before.