Modern internet technologies have revolutionized traditional education by providing flexible and resourceful e-learning opportunities in all fields of life. Programming is an integral part of the undergraduate curriculum in computer sciences where an adequate level of programming expertise is expected from the graduates. In this paper, we explore and examine the key factors that contribute to developing programming skills among undergraduate students in e-learning. We propose that programming education follows the Technology Acceptance Model (TAM), which affects the students' attitude toward learning. We extend the TAM by integrating the factors of teaching practices, intrinsic factors, perceived usefulness, and efficacy problems with the learning intentions in our research framework. This research involves the responses of the 460 final year students studying for a Bachelor of Computer Science and Software Engineering at an e-learning institution. Structural Equation Modelling (SEM) and Confirmatory Factor Analysis (CFA) have been employed to evaluate the relationship between factors of the model. Experimental results demonstrate that teaching practices, intrinsic factors, and perceived usefulness play a key role in endorsing learning intentions in the students. Further analysis reveals that learning intentions positively influence the programming expertise whereas an adverse impact has been observed from the efficacy problems. The results proclaim that perceived usefulness, teaching practices, and intrinsic factors develop adequate learning intentions in the students which overcome the efficacy problems and lead to better programming expertise. This research provides critical implications for policymakers to effectively implement computer science programs in an e-learning paradigm.