Depression is a psychological state of mind that often influences a person in an unfavorable manner. While it can occur in people of all ages, students are especially vulnerable to it throughout their academic careers. Beginning in 2020, the COVID-19 epidemic caused major problems in people’s lives by driving them into quarantine and forcing them to be connected continually with mobile devices, such that mobile connectivity became the new norm during the pandemic and beyond. This situation is further accelerated for students as universities move towards a blended learning mode. In these circumstances, monitoring student mental health in terms of mobile and Internet connectivity is crucial for their wellbeing. This study focuses on students attending an International University of Bangladesh to investigate their mental health due to their continual use of mobile devices (e.g., smartphones, tablets, laptops etc.). A cross-sectional survey method was employed to collect data from 444 participants. Following the exploratory data analysis, eight machine learning (ML) algorithms were used to develop an automated normal-to-extreme severe depression identification and classification system. When the automated detection was incorporated with feature selection such as Chi-square test and Recursive Feature Elimination (RFE), about 3 to 5% increase in accuracy was observed by the method. Similarly, a 5 to 15% increase in accuracy has been observed when a feature extraction method such as Principal Component Analysis (PCA) was performed. Also, the SparsePCA feature extraction technique in combination with the CatBoost classifier showed the best results in terms of accuracy, F1-score, and ROC-AUC. The data analysis revealed no sign of depression in about 44% of the total participants. About 25% of students showed mild-to-moderate and 31% of students showed severe-to-extreme signs of depression. The results suggest that ML models, incorporating a proper feature engineering method can serve adequately in multi-stage depression detection among the students. This model might be utilized in other disciplines for detecting early signs of depression among people.