Over the past few years, several microring resonator (MRR)-based analog photonic architectures have been proposed to accelerate general matrix-matrix multiplications (GEMMs), which are found in abundance in deep learning workloads. These architectures have dramatically grown in popularity because they offer exceptional throughput and energy efficiency compared to their electronic counterparts. However, such architectures, due to their traditional realization based on the silicon-on-insulator (SOI) material platform, face two shortcomings. First, the high-index contrast of the SOI platform incurs high scattering losses, which mandates the provisioning of high optical input power. Second, SOI waveguides are susceptible to two-photon absorption (TPA), which can incur substantial optical signal losses at moderate-to-high signal fan-in. These shortcomings have severely detrimental effects on the achievable parallelism, throughput, and energy efficiency of SOI MRR-based GEMM accelerators. To address these shortcomings, we present a novel Silicon Nitride (SiN)-Based Photonic GEMM Accelerator called SiNPhAR. SiNPhAR architecture employs SiN-based active and passive devices to implement analog GEMM functions. Since the SiN material does not exhibit high-index contrast and TPA, the optical signal losses in our SiNPhAR architecture are very low. This advantage significantly enhances the achievable processing parallelism, throughput, and energy efficiency of the SiNPhAR architecture, compared to SOI-based photonic GEMM accelerators from prior work. We quantify and compare these benefits of SiNPhAR architecture via our cross-layer evaluation for a benchmark workload comprising four modern deep neural network models. From the system-level performance analysis, SiNPhAR demonstrates at least 1.7x better throughput (frames-per-second (FPS)) while consuming at least 2.8x better energy efficiency (FPS/W) than prior SOI-based GEMM accelerators.