Chronic Bronchitis: This is a likely diagnosis given the patient's persistent productive cough. Although the patient has no history of smoking, chronic bronchitis can also be caused by long-term exposure to air pollutants, dust, or other environmental factors. The lack of response to mucolytics or expectorants does not rule out this diagnosis, as these treatments may provide symptomatic relief but not address the underlying cause.

Asthma: Asthma can cause a chronic cough, and the diagnosis should be considered, especially if the cough is worsening at night or with exercise. The absence of shortness of breath does not rule out asthma, as cough can be a predominant symptom.
Gastroesophageal Reflux Disease (GERD): GERD can cause a chronic cough due to acid reflux irritating the airways. The patient's lack of response to mucolytics or expectorants and the absence of other symptoms like fever or weight loss make this a plausible diagnosis.
Allergic Rhinitis or Sinusitis: Postnasal drip from allergic rhinitis or sinusitis can cause a persistent cough. The patient's symptoms of a productive cough without fever or weight loss could be consistent with this diagnosis.

Lung Cancer: Although less likely given the patient's lack of smoking history and absence of weight loss or other systemic symptoms, lung cancer must be considered, especially if the chest X-ray shows any abnormalities. It's crucial to not miss this diagnosis due to its significant implications.
Tuberculosis (TB): TB can present with a chronic cough and may not always be accompanied by systemic symptoms like fever or weight loss, especially in its early stages. Given the potential severity and public health implications, TB should not be missed.
Pulmonary Embolism: While less common as a cause of chronic cough, pulmonary embolism can present with a cough and should be considered, especially if there are any risk factors for thromboembolic disease.

Cystic Fibrosis: Although typically diagnosed in childhood, cystic fibrosis can occasionally present in adulthood, especially in milder forms. It would be an unusual cause of a new onset of symptoms in a 50-year-old but should be considered if other diagnoses are ruled out.
Bronchiectasis: This condition involves permanent dilation of parts of the airways and can cause a chronic productive cough. It might be considered if the patient has a history of recurrent infections or other underlying conditions that could lead to bronchiectasis.
Sarcoidosis: Sarcoidosis is a condition that can affect multiple parts of the body, including the lungs, and can cause a chronic cough among other symptoms. It would be a less common diagnosis but should be considered if other tests and evaluations suggest its presence.