The COVID-19 pandemic has highlighted a significant research gap in the field of molecular diagnostics. This has brought forth the need for AI-based edge solutions that can provide quick diagnostic results whilst maintaining data privacy, security and high standards of sensitivity and specificity. This paper presents a novel proof-of-concept method to detect nucleic acid amplification using ISFET sensors and deep learning. This enables the detection of DNA and RNA on a low-cost and portable lab-on-chip platform for identifying infectious diseases and cancer biomarkers. We show that by using spectrograms to transform the signal to the time-frequency domain, image processing techniques can be applied to achieve the reliable classification of the detected chemical signals. Transformation to spectrograms is beneficial as it makes the data compatible with 2D convolutional neural networks and helps gain significant performance improvement over neural networks trained on the time domain data. The trained network achieves an accuracy of 84% with a size of 30kB making it suitable for deployment on edge devices. This facilitates a new wave of intelligent lab-on-chip platforms that combine microfluidics, CMOS-based chemical sensing arrays and AI-based edge solutions for more intelligent and rapid molecular diagnostics.