Final answer:
A CT scan or an MRI is the next step after unsuccessful syringing and probing to diagnose a complete block, potentially followed by a biopsy if a tumor is suspected.
Step-by-step explanation:
When syringing and probing have not identified the cause of a complete block, the next best step to diagnose the issue further would be to perform a computed tomography (CT) scan or a magnetic resonance imaging (MRI). A CT scan provides detailed X-ray images and could help in locating the block, whereas an MRI uses magnetic fields to generate images of soft tissues and might be more suitable depending on the nature of the blockage. If these imaging techniques suggest the presence of a tumor or abnormal tissue, a biopsy may then be necessary to confirm the diagnosis by examining the tissue microscopically.