The Reconfigurable Intelligent Surface (RIS) constitutes one of the prominent technologies for the next 6-th Generation (6G) of wireless communications. It is envisioned to enhance signal coverage in cases where obstacles block the direct communication from Base Stations (BSs), and when high carrier frequencies are used that are sensitive to attenuation losses. In the literature, the exploitation of RISs is exclusively based on traditional coherent demodulation, which necessitates the availability of Channel State Information (CSI). Given the CSI, a multi-antenna BS or a dedicated controller computes the pre/post spatial coders and the RIS configuration. The latter tasks require significant amount of time and resources, which may not be affordable when the channel is time-varying or the CSI is not accurate enough. In this paper, we consider the uplink between a single-antenna user and a multi-antenna BS and present a novel RIS-empowered Orthogonal Frequency Division Multiplexing (OFDM) communication system based on the differential phase shift keying, which is suitable for high noise and/or mobility scenarios. Considering both an idealistic and a realistic channel model, analytical expressions for the Signal-to-Interference and Noise Ratio (SINR) and the Symbol Error Probability (SEP) of the proposed non-coherent RIS-empowered system are presented. Our extensive computer simulation results verify the accuracy of the presented analysis and showcase the proposed system's performance and superiority over coherent demodulation in different mobility and spatial correlation scenarios.