To address the reliance of most deep learning methods for magnetic resonance (MR) imaging (MRI) reconstruction on extensive fully-sampled datasets for training, this study proposes an unsupervised dual-domain N2N network with attention mechanisms (DN2NA) for parallel MRI reconstruction. The proposed DN2NA network can directly reconstruct undersampled k-space data without requiring additional training data. Specifically, we integrate complex-valued convolution and channel attention mechanism into the N2N framework to construct a baseline unsupervised network N2NA. Two physical priors are incorporated to enhance the performance of the frequency-domain (k-space) N2NA network, which is then cascaded with an image-domain N2NA network to form the dual-domain DN2NA architecture. This combination effectively leverages the complementary advantages of frequency-domain and image-domain networks. Given the absence of ground-truth references in practical scenarios, an early-stopping strategy is adopted to prevent overfitting and improve stability. Experiments conducted on three knee and brain datasets demonstrate that DN2NA achieves higher PSNR and SSIM, along with lower HFEN and STD compared to existing unsupervised networks (IUNN and KUNN), indicating superior reconstruction quality and stability in repeated reconstructions. Furthermore, DN2NA exhibits comparable or better performance than the supervised network MICCAN.