We introduce the Simulated Environment for Neurocognitive State Evaluation (SENSE-42), a multimodal dataset collected during user interactions with desktop computers. It is designed for studying spontaneous fluctuations in the neurocognitive state related to the tonic alertness of computer users, with recordings from 42 participants over 2-hour sessions. Within a simulated desktop environment, participants performed real-world routine tasks, including application switching, file management, typing, and web browsing. High-resolution data were recorded across physiological (electroencephalography, electrocardiography, respiration) and subjective modalities of alertness. At five-minute intervals, alertness state was reported using seven questions, addressing sleepiness (Karolinska Sleepiness Scale), mental and temporal demand, perceived performance, effort and frustration (NASA Task Load Index), as well as attentiveness. Behavioural data included keyboard, mouse and webcam inputs. Demographic information for the experience, habits, and preferences of computer usage was collected. In addition, individual differences in sleep quality were evaluated using the Pittsburgh Sleep Quality Index and the Epworth Sleepiness Scale. The SENSE-42 dataset can contribute to future research in user state monitoring, behavioural analysis and physiological computing.