Driving continuous, low-power artificial intelligence (AI) in the Internet of Things (IoT) requires reliable energy harvesting and storage under indoor or low-light conditions, where batteries face constraints such as finite lifetimes and increased environmental impact. Here, we demonstrate an integrated three-terminal dye-sensitized photocapacitor that unites a dye-sensitized solar cell (DSC) with an asymmetric supercapacitor, leveraging molecularly engineered polyviologen electrodes and bioderived fungal-based membranes. Under 1000 lux ambient illumination, the photocapacitor delivers photocharging voltages of 920 mV, achieving power conversion efficiencies exceeding 30% and photocharging efficiencies up to 18%. Density Functional Theory calculations reveal low reorganization energies (0.1-0.2 eV) for polyviologen radical cations, promoting efficient charge transfer and stable cycling performance over 3000 charge-discharge cycles. The system reliably powers a multilayer IoT network at 500 lux for 72 hours, surpassing commercial amorphous-silicon modules by a factor of 3.5 in inference throughput. Critically, the photocapacitor driven edge microcontroller achieves 93% accuracy on CIFAR-10 classification with an energy requirement of only 0.81 mJ per inference. By eliminating the need for batteries or grid connection, this work offers a proof of concept for high-efficiency, long-lived indoor power solutions that merge advanced materials chemistry with edge AI, demonstrating a practical route toward self-sustaining, data-driven IoT devices.