Mild cognitive impairment (MCI) is a neurological disease which is often comorbid with early stages of Alzheimer's disease (AD). This study explores the potential for detecting changes in neurological functional organization which may be indicative of MCI and early AD using neural network models for scalp EEG signal reconstruction. Resting 32-channel EEG records from 48 age-matched participants (mean age 75.7 years) - 15 normal controls (NC), 16 MCI, and 17 early-stage AD - are examined. Neural network models are trained to reconstruct artificially 'deleted' samples of EEG using subsets of records from NC participants. Models are applied to EEG records and quality scores are assigned to reconstructions of individual channels. Principal components of regional average reconstruction quality scores are used in a support vector machine model to discriminate between groups. Analyses demonstrate accuracies of 90.3% for MCI vs. NC (p-value<0.0005), 90.6% for AD vs. NC (p-value<0.0003), and 87.5% for AD/MCI vs. NC (p-value<0.0003). Techniques developed here may be used to detect changes in EEG activity due to neurological degeneration associated with MCI and early AD.