Is the sentence 他原来什么都不知道 grammatically correct? "他原来什么都不知道"

Shouldn't it be 他原来什么都没(有)知道 to show that we're talking about the past tense here?
Strictly speaking, the adverb 没 does not negate events that happened in the past, rather it is used to express negative completed actions. When we say completed we mean that the action indicated by the predicate it's finished, it doesn't necessarily mean that is a past tense. 没 is the negative counterpart of 了 (when it is the aspectual particle).

Both 了 and 没 should only be used if the predicate in your sentence expresses a true action, in other words, if the verb does something to an object, acts directly upon it or changes it in some way. The predicate 知道 (to know) doesn't indicate an action, because the object of your knowledge doesn't undergo or suffer any change at all. In these situations should use 不 instead.

Of course, if you use 不 you should express the time through some adverb, if you want to keep the notion of past tense in your sentence. The word 原来 can be used as an adverb (originally) or as an adjective (original, initial) and it describes an original condition. If the meaning you had in mind was "At first he didn't know anything", then your translation (他原来什么都不知道) is perfectly fine. However if you wanted to say "He didn't know anything before." (which is a little bit different from the previous one), you should consider using the adverb 以前. So, the sentence


  他以前什么都不知道。


is correct too. It certainly indicates a past tense and you don't put 没 because of the nature of the predicate. But, again, it depends on the interpretations.