What would cause a Briggs and stratton 4.5 HP lawn mower from starting?

If it will start but dies like it is running out of gas, it is most likely the small o ring that the float needle goes into. The new gas mixture that has been forced on that mixes alcohol in the gas and causes that o ring to swell and effectively shuts the gas off too early not allowing the float bowl to fill up. The cure is a carb overhaul kit for around $8. You cannot buy the o-ring separate and I have not found any substitutes that can handle this new federally mandated abuse forced upon us.

After installing the new o-ring use sta-bill on the gas this supposed to help but I wouldn't count on it too much try to run the gas out of the carb or drain it if not being used for a long period.