If I were to write a date out in alphabetical form rather than numeral (e.g. nineteen-thirty-four as opposed to 1934), would it be Nineteen-Thirty-Four or nineteen-thirty-four? Thanks in advance.
I can't see you needing a hyphen between nineteen and thirty. Nineteen thirty-four (also the same format for hours/minutes.) I'm still trying to check that.
SwampDog is correct. The only hyphen that's needed goes between "thirty" and "four." Also, nothing is capitalized unless you're beginning a sentence with "nineteen."
Lower case, however, unless the year is at the beginning of the sentence (in which case you'd capitalize the first word) the CMoS recommends using numerals. Here's what the CMoS says exactly (point 9.30): "Years are expressed in numerals unless they stand at the beginning of a sentence, in which case rewording may be a better option." There is no example in the Chicago Manual of Style with regards to writing out years because they recommend to never do it.