Foundation models have shown strong generalization across scientific domains, but their use in power systems remains largely task-specific. We investigate whether a pretrained tabular foundation model (TFM), TabPFN, can serve as a general-purpose neural solver for power grid steady-state analysis. We evaluate the TFM on three tasks: power flow (PF) prediction, N-k contingency screening (NCS), and voltage stability margin (VSM) prediction. We performed experiments on 118- and 2000-bus systems, comparing the TFM against task-specific neural baselines. Without retraining or fine-tuning, the TFM matches or outperforms the best task-specific model in several settings across the three tasks. For 118-bus PF prediction, a variant of the TFM achieves errors of $1\times 10^{-3}$ pu for voltage magnitudes and $0.30^\circ$ for voltage angles, outperforming all baselines. On unseen N-1 contingency and close-to-infeasible PF cases, the TFM is competitive with the DCPF approximation. For millions of unseen N-2 contingencies, the TFM achieves AUCs of 0.92 and 0.95 for branch and voltage violation screening, respectively. The TFM also attains accurate VSM prediction performance for the 2000-bus system with limited labelled data. The TFM attains strong results across the tested tasks despite pretraining without any power-system-specific dataset and requiring no fine-tuning step. These results offer a glimpse into the potential of pretrained TFMs as a neural solver for a range of power grid analysis tasks.

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