The massiveness of devices in crowded Machine-to-Machine (M2M) communications brings new challenges to existing random-access (RA) schemes, such as heavy signaling overhead and severe access collisions. In order to reduce the signaling overhead, we propose a fixed-symbol aided RA scheme where active devices access the network in a grant-free method, i.e., data packets are directly transmitted in randomly chosen slots. To further address the access collision which impedes the activity detection, one fixed symbol is inserted into each transmitted data packet in the proposed scheme. An iterative message passing based activity detection (MP-AD) algorithm is performed upon the received signal of this fixed symbol to detect the device activity in each slot. In addition, the deep neural network-aided MP-AD (DNN-MP-AD) algorithm is further designed to alleviate the correlation problem of the iterative message passing process. In the DNN-MP-AD algorithm, the iterative message passing process is transferred from a factor graph to a DNN. Weights are imposed on the messages in the DNN and further trained to improve the accuracy of the device activity detection. Finally, numerical simulations are provided for the throughput of the proposed RA scheme, the accuracy of the proposed MP-AD algorithm, as well as the improvement brought by the DNN-MP-AD algorithm.