Sperm cell motility and morphology observed under the bright field microscopy are the only criteria for selecting a particular sperm cell during Intracytoplasmic Sperm Injection (ICSI) procedure of Assisted Reproductive Technology (ART). Several factors such as oxidative stress, cryopreservation, heat, smoking and alcohol consumption, are negatively associated with the quality of sperm cell and fertilization potential due to the changing of subcellular structures and functions which are overlooked. However, bright field imaging contrast is insufficient to distinguish tiniest morphological cell features that might influence the fertilizing ability of sperm cell. We developed a partially spatially coherent digital holographic microscope (PSC-DHM) for quantitative phase imaging (QPI) in order to distinguish normal sperm cells from sperm cells under different stress conditions such as cryopreservation, exposure to hydrogen peroxide and ethanol. Phase maps of total 10,163 sperm cells (2,400 control cells, 2,750 spermatozoa after cryopreservation, 2,515 and 2,498 cells under hydrogen peroxide and ethanol respectively) are reconstructed using the data acquired from the PSC-DHM system. Total of seven feedforward deep neural networks (DNN) are employed for the classification of the phase maps for normal and stress affected sperm cells. When validated against the test dataset, the DNN provided an average sensitivity, specificity and accuracy of 85.5%, 94.7% and 85.6%, respectively. The current QPI + DNN framework is applicable for further improving ICSI procedure and the diagnostic efficiency for the classification of semen quality in regard to their fertilization potential and other biomedical applications in general.