With the increasing size of floating offshore wind turbines (FOWTs), stall-induced aeroelastic instability has become a critical issue. This study numerically investigates this instability for FOWTs at stand-still conditions using time and frequency domain approaches. A nonlinear aeroelastic model based on quasi-steady theory and a linearized version are used for time and frequency domain simulations, respectively. Hydrodynamic damping considers both radiation and viscous drag effects. The aeroelastic instability of a stand-still NREL OC3-Hywind 5MW FOWT is analyzed for various inflow yaw misalignment angles. Frequency domain simulation shows rotor edgewise and tower side-side modes exhibit stall-induced instability due to aerodynamic negative damping at specific yaw misalignment and azimuth angles. The platform's yaw mode also shows small negative damping, despite large hydrodynamic damping, while other platform modes remain dynamically stable. Safety margins of FOWTs are analyzed for multi-mode stability, and an active control strategy is proposed to prevent stall-induced instability in all unstable modes. Limit cycle oscillations in the rotor's in-out plane are observed from time domain simulation. Instability regions predicted by both analyses highly overlap, but frequency domain results are more conservative. Blade instability may cause high-frequency vibrations in platform movements with limited amplitudes and severe oscillations in tower structures.