Studies recently accomplished on the Enteric Nervous System have shown that chronic degenerative diseases affect the Enteric Glial Cells (EGC) and, thus, the development of recognition methods able to identify whether or not the EGC are affected by these type of diseases may be helpful in its diagnoses. In this work, we propose the use of pattern recognition and machine learning techniques to evaluate if a given animal EGC image was obtained from a healthy individual or one affect by a chronic degenerative disease. In the proposed approach, we have performed the classification task with handcrafted features and deep learning based techniques, also known as non-handcrafted features. The handcrafted features were obtained from the textural content of the ECG images using texture descriptors, such as the Local Binary Pattern (LBP). Moreover, the representation learning techniques employed in the approach are based on different Convolutional Neural Network (CNN) architectures, such as AlexNet and VGG16, with and without transfer learning. The complementarity between the handcrafted and non-handcrafted features was also evaluated with late fusion techniques. The datasets of EGC images used in the experiments, which are also contributions of this paper, are composed of three different chronic degenerative diseases: Cancer, Diabetes Mellitus, and Rheumatoid Arthritis. The experimental results, supported by statistical analysis, shown that the proposed approach can distinguish healthy cells from the sick ones with a recognition rate of 89.30% (Rheumatoid Arthritis), 98.45% (Cancer), and 95.13% (Diabetes Mellitus), being achieved by combining classifiers obtained both feature scenarios.