This paper investigates simultaneous wireless information and power transfer (SWIPT)-enabled cell-free massive multiple-input multiple-output (CF-mMIMO) networks with power splitting (PS) receivers and non-orthogonal multiple access (NOMA). By exploiting the conjugated beamforming method, the closed-form expressions of the information rate and the total harvested power at each user equipment (UE) are derived. To improve the system spectral efficiency, a sum rate maximization problem is formulated subjecting to the quality of service requirement at each UE and the power budget constraint at each access point by optimizing the UE clustering, the power control coefficients, and the PS ratios. To solve the formulated non-convex and mixed combinatorial problem, a machine learning-based approach is designed. Particularly, the UE clustering is first optimized by using a K-means based method and then the power control coefficients and the PS ratios are jointly optimized by a proposed multi-agent deep Q-network (MA-DQN) based method. The impact of the discount factor of the MA-DQN based method on the derived result is discussed. It is proved that by setting the discount factor as zero, the performance loss is negligible. Based on this observation, a zero-discount MA-DQN (0- $\gamma$ MA-DQN) based method is further proposed to improve the computational efficiency. Also, the computational complexity of the proposed machine learning-based approach is analyzed. Simulation results show that the proposed machine learning-based approach outperforms various existing approaches. Moreover, it indicates that CF-mMIMO and NOMA could enhance the propagation performance of SWIPT while the proposed machine learning-based approach could facilitate resource allocation.