The 14ST would be a self-propelled tri-cycler walk-behind, so manual engaging BBC.
Two items - either engine can't handle the load (mixture is off, weak spark, speed is too low, etc) or there is something binding up in the BBC which is placing an excessive load on the engine when engaged.
Try this (may require two people): Remove spark plug. Then have helper engage BBC lever and tip mower up while you turn the blade (or use pull starter) - does everything rotate freely? If not, then see why not.
If the engine does turn freely, I'd drop the carb bowl and make sure that everything is clean - and then do a standard tune-up. Check throttle shaft for stickiness, check plug, air filter, and so on. If your air-fuel mixture is too far off one way or the other, it could do what you are describing. Also you may want to try fresh gas.