Q: Car shakes, refuses to accelerate, then cuts off.

Based on the information you provided, It sounds like you may have a throttle position sensor issue. The throttle position sensor tells the computer how much throttle you are giving the engine. Sometimes the sensor wears out and has dead spots that do not send the proper information. Your vehicle gets confused and defaults back to an idle setting. If you press the throttle, you give the motor access to more air, but the position sensor may not tell the computer to add more fuel. The result is a rough running motor that will stall if more throttle is applied. Engine heat creates more electrical resistance within the component and combined with the already bad internal connections, this will make it worse as the vehicle warms up.

Your steering wheel and brakes rely on the vehicle running properly, so when it shuts off, you no longer have steering assistance or enough vacuum to help with braking. It is also possible that the pedal position sensor is the problem. It has very similar symptoms, but generally does not get worse as the vehicle warms up. I suggest having a certified technician, like one from YourMechanic, determine the exact cause of your stalling issue and driving symptoms. Afterwards they’ll be able to provide you with a quote for repairs.