In the sentence "There was no list of answers in the back of the book" identifying the verb is pretty simple. Obviously, the verb is "was", which is a past tense of the "be"-verb in English.
Identifying the subject of this sentence is a bit tricky because the word "There" occupies the place usually reserved for the subject of an English sentence. The word "there," however, is an adverb and as such it should not be identified as the subject.
Instead, the word "list" is the subject of "was" and the word "no" is an adjective modifying the noun "list." In this sentence, the verb "was" is being used in an existential sense. What the sentence actually says is that "No list of answers existed (or was present) there in the back of the book."
So, in this sentence, I would say that "was" is the verb and "list" is the subject.