This paper presents a novel and effective deep reinforcement learning (DRL)-based approach to addressing joint resource management (JRM) in a practical multi-carrier non-orthogonal multiple access (MC-NOMA) system, where hardware sensitivity and imperfect successive interference cancellation (SIC) are considered. We first formulate the JRM problem to maximize the weighted-sum system throughput. Then, the JRM problem is decoupled into two iterative subtasks: subcarrier assignment (SA, including user grouping) and power allocation (PA). Each subtask is a sequential decision process. Invoking a deep deterministic policy gradient algorithm, our proposed DRL-based JRM (DRL-JRM) approach jointly performs the two subtasks, where the optimization objective and constraints of the subtasks are addressed by a new joint reward and internal reward mechanism. A multi-agent structure and a convolutional neural network are adopted to reduce the complexity of the PA subtask. We also tailor the neural network structure for the stability and convergence of DRL-JRM. Corroborated by extensive experiments, the proposed DRL-JRM scheme is superior to existing alternatives in terms of system throughput and resistance to interference, especially in the presence of many users and strong inter-cell interference. DRL-JRM can flexibly meet individual service requirements of users.