In this paper, we study an uplink reconfigurable intelligent surfaces-non-orthogonal multiple access (RIS-NOMA) assisted mobile edge computing (MEC) network with simultaneous wireless information and power transfer (SWIPT), where the users want to offload their computing tasks to the BS via a RIS and a relay based on the SWIPT technique. The goal of the paper is to minimize the delay concerning the computing tasks of the users by jointly optimizing the power allocation ratio, the phase shift matrix of the RIS, the offloading task ratio, and the offloading transmit power. For solving the challenging optimization problem, we conceive a low-complexity algorithm by optimizing two subproblems separately, based on the penalty method as well as the successive convex approximation. Simulation results demonstrate that the proposed RIS-NOMA assisted MEC network with SWIPT outperforms both the conventional RIS-NOMA assisted MEC network without SWIPT and the RIS-orthogonal multiple access assisted MEC network.