Background COVID-19 has spread like wildfire across the globe, prompting many governments to impose unprecedented stay-at-home orders to limit its transmission. During an extended stay-at-home period, individuals may engage in more online leisure activities. Internet use is a double-edged sword that may have both desirable and undesirable effects on psychological well-being, and this study sought to disentangle adaptive from maladaptive internet use amidst this unusual health crisis. Objective The objectives of this study were to assess the prevalence of probable depression during the COVID-19 stay-at-home period and to test three hypothesized risk reduction or risk elevation mechanisms, namely social capital–accrual, escape-from-self, and time-displacement effects. Methods This study took place from March to May 2020 at the early stage of the pandemic. The study adopted a prospective design, with an online survey administered to 573 UK and 474 US adult residents at two assessment points 2 months apart. Results The prevalence of moderate to severe depression was 36% (bootstrap bias-corrected and accelerated [BCa] 95% CI 33%-39%) at Time 1 (ie, initial time point) and 27% (bootstrap BCa 95% CI 25%-30%) at Time 2 (ie, follow-up time point). The results supported the social capital–accrual hypothesis by showing that the approach coping style was inversely associated with Time 2 depression through its positive associations with both social networking and perceived family support. The results also supported the escape-from-self hypothesis by revealing that the avoidant coping style was positively associated with Time 2 depression through its positive associations with both gaming and cyberbullying victimization, but the serial mediation model was no longer significant after Time 1 depression and some demographic risk factors had been controlled for. Finally, the results supported the time-displacement hypothesis by showing that gaming was positively associated with Time 2 depression through its inverse associations with social networking and perceived family support. Conclusions During the extended stay-at-home period in the early stages of the COVID-19 pandemic, the prevalence of probable depression during the 2-month study period was high among the UK and US residents. Individuals with distinct coping styles may engage in different types of online leisure activities and perceive varying levels of social support, which are associated with risks of probable depression.