The first version of both examples is correct. In the second version of your examples you have a double negative. If you expand the contractions it becomes a bit more clear, i.e. "I would not neither understand nor believe in what I saw...". In addition to being incorrect, the double negatives would cancel each other out and change the meaning of the sentence.
“Me neither.” or “Me either”
Tim,
The first version of both examples is correct. In the second version of your examples you have a double negative. If you expand the contractions it becomes a bit more clear, i.e. "I would not neither understand nor believe in what I saw...". In addition to being incorrect, the double negatives would cancel each other out and change the meaning of the sentence.
Ian