I just had a chest x-ray that showed minimal old granulomatous disease. Could this cause shortness of breath with minimal exercise (walking up hill)?

Shouldn't. If the lung involvement is truly "minimal" on CXR or CT scan then this shouldn't compromise your lung function enough to cause respiratory symptoms with minimal exercise. Important to determine etiology of lesions first then look for other causes of shortness of breath. Deconditioning, asthma, heart disease are just a few conditions that can be implicated. See Pulmonologist for further evaluation.