The correct answer to this open question is the following.
I think it was not appropriate for Marshall to hear and decide on this case considering his involvement in the circumstances of the case. Of course, he had to be biased because he was a member of the cabinet of President John Adams as the Secretary of State, but also he was a judge. These dual roles were played by John Marshall as both the Secretary of State that failed to deliver Marbury’s commission and as the Chief Justice involved with deciding this case.
In the case of Marbury v Madison of 1803, the Supreme Court established for the first time the important principle of judicial review. This concept of judicial review allowed the US Supreme Court to declare the unconstitutionality of legislation created by Congress or the President.
John Marshall, Chief Justice, was the judge who wrote the unanimous opinion that decided the case.