"no" can be an adverb or an adjective. "without" is a preposition, so "no" and "without" are very different words and don't have any relation between themselves. The only similarity between "no" and "without" is that "without" is the negative form of "with", so both words are used to express a negation. You can replace "without" by "no" if you reconstruct the phrase so that the phrase doesn't need a preposition anymore. So, your phrase "My investigations were without result" can be replaced by "My investigations had no results." because this second phrase doesn't require a preposition, this doesn't mean that "no" and "without" are synonyms, they are completely different words because one is a preposition and the other is an adjective in this example.

Without is like 没有, but no is more diverse and has many equivalents in Chinese. If you wanted to use "no“ in this sentence you'd say "My investigations had no results."

Your sentence can use no. Here is a time you can not rep ace without- so there must be more... I am going without any, This would be replaced with none: I will have none. But no does not work unless you name the subject. I will have no _________.