No Objection mail to potential advisor before mailing another in the same department
i Don’t understand the reason for the original admonishment, except if it’s based on the assumption that the professors might talk and thus decide to reject you from both groups. However, even given that, since the first professor has already said he can’t take on new students, there isn’t any reason you can’t still contact the others. You don’t need to ask the professor if there are no objections: the professor’s already done that by turning you down outright. The worst that can happen is that they will say no.