* Seized Compressor: If the AC compressor bearing completely fails and seizes, the compressor will lock up. This will put significant strain on the serpentine belt. The belt might break, or the crankshaft pulley might be damaged.
* Belt Breakage: A broken serpentine belt prevents many engine components from operating, including the alternator (which charges the battery) and the power steering pump. If the battery is already low, a broken belt could prevent the car from starting because it lacks sufficient power to crank the engine.
* Other Causes More Likely: There are far more common reasons why a car won't start. A dead battery, faulty starter, bad alternator, ignition problems, or fuel delivery issues are much more probable causes than a seized AC compressor.
In short: While a completely failed AC compressor bearing *could* lead to a broken serpentine belt and prevent starting due to a dead battery, it's an indirect and relatively uncommon cause of a no-start condition. A mechanic would likely find other problems before identifying a seized AC compressor as the root cause of the no-start.
