We present a model for digital neural impairment screening and self-assessment, which can evaluate cognitive and motor deficits for patients with symptoms of central nervous system (CNS) disorders, such as mild cognitive impairment (MCI), Parkinson’s disease (PD), Huntington’s disease (HD), or dementia. The data was collected with an Android mobile application that can track cognitive, hand tremor, energy expenditure, and speech features of subjects. We extracted 238 features as the model inputs using 16 tasks, 12 of them were based on a self-administered cognitive testing (SAGE) methodology and others used finger tapping and voice features acquired from the sensors of a smart mobile device (smartphone or tablet). Fifteen subjects were involved in the investigation: 7 patients with neurological disorders (1 with Parkinson’s disease, 3 with Huntington’s disease, 1 with early dementia, 1 with cerebral palsy, 1 post-stroke) and 8 healthy subjects. The finger tapping, SAGE, energy expenditure, and speech analysis features were used for neural impairment evaluations. The best results were achieved using a fusion of 13 classifiers for combined finger tapping and SAGE features (96.12% accuracy), and using bidirectional long short-term memory (BiLSTM) (94.29% accuracy) for speech analysis features.