Is there an undecidable decision problem that computable algorithm for it leads to an algorithm for halting problem?
Let me rephrase your question. Suppose $O$ is undecidable; can Turing machines with an $O$-oracle solve the halting problem? There are some undecidable $O$ for which this is false. Constructing such $O$ is known as Post's problem, solved using the priority method; Wikipedia has some details.