Chronic Bronchitis: Given the patient's age and history of a chronic persistent cough that has been treated with antibiotics and steroids, chronic bronchitis is a likely diagnosis. The recurrence of the cough and the presence of a severe productive cough suggest a chronic condition.

Pneumonia: The patient's symptoms of a severe productive cough and significant weakness could indicate pneumonia, especially since he has not responded to doxycycline.
Asthma or COPD Exacerbation: The patient's history of a chronic cough and the recent exacerbation could be related to asthma or COPD, especially if he has a history of these conditions.
Gastroesophageal Reflux Disease (GERD): GERD can cause a chronic cough, and the patient's symptoms could be related to this condition, especially if he has a history of heartburn or acid reflux.

Lung Cancer: Although less likely, lung cancer is a critical diagnosis that should not be missed, especially in an 84-year-old patient with a chronic cough and significant weakness.
Pulmonary Embolism: A pulmonary embolism can cause a sudden onset of a cough and weakness, and it is a life-threatening condition that requires immediate attention.
Tuberculosis: Although less common, tuberculosis can cause a chronic cough and should be considered, especially if the patient has been exposed to someone with TB or has a history of travel to an area where TB is common.

Sarcoidosis: This is a rare condition that can cause a chronic cough and should be considered if other diagnoses have been ruled out.
Bronchiectasis: This is a condition where the airways are damaged, leading to a chronic cough and recurrent infections.
Interstitial Lung Disease: This is a group of conditions that affect the lung tissue and can cause a chronic cough, although it is less likely in this patient.