Your first example sentence doesn't really work at all. The second one is a properly constructed sentence. But it sounds extremely formal and dated and it repeats unneeded words. I would suggest wording it much more simply: I don't have enough time to watch the movie or to sleep. If you insist on including neither and nor (and you want to sound like a character from one of Shakespeare's plays), at least don't repeat the unneeded words: Neither do I have time to watch the movie nor to sleep.

It is more natural to say "I have no time to watch the movie or to sleep." Neither... nor... is no longer used very often nowadays. No worries! :)

If you use a negative phrase like " no time" you have to use either / or and if you are referring to a general situation rather than a specific movie , you should say " I have no time to either watch movIES or sleep " Neither / nor is used with an affirmative verb . I neither have time to watch movies nor sleep