This paper investigates an uplink cooperative Non-Orthogonal Multiple Access (NOMA) system integrated with energy harvesting in ultra-dense wireless networks, where both base stations (BSs) and users are spatially modeled as independent Poisson Point Processes (PPPs). A distance-dependent cooperative transmission scheme is proposed, allowing a near user to assist a far user only when their separation is below a predefined threshold, thus improving cooperation efficiency and reducing unnecessary relay operations. The near user allocates a fraction ϵ of its harvested energy to relay the far user's signal, while the remaining (1−ϵ) portion is used for its own uplink transmission. Using the stretched path loss model and Campbell's theorem, a closed-form expression for the average harvested energy is derived, and system capacity is evaluated through Monte Carlo simulations. Results show that the proposed energy-harvesting cooperative NOMA (EH-C-NOMA) scheme significantly improves network performance, achieving up to 85% higher capacity than the non-cooperative case and 11.63% improvement over full cooperation.