It cranks but sounds and feels like it is not "catching" to start?

I received a used car listed above ZTS PZEV 2.3l and ran very well until a few days ago. It cranks but sounds and feels like it is not "catching" to start. When looked under the hood, there is a broken/missing plastic piece (looks like two plastic levers-- one white and other is black) behind the air intake and near the throttle body. When it is pressed down or another person pressing while one starts the engine, it will start the car. Also, it appears to occur more on cold starts, easing up throughout the day. I cannot find any reference to this in my Haynes guide nor find the correct term to research on forums or online parts stores. So, my question is, is this part of the actual throttle body and the whole thing need to be replaced? Is it the throttle actuator itself? I do not have any previous repair info on the vehicle, if this was a prior issue or ignored until I took the vehicle. I would appreciate any help with what the actual part is called, possible causes of failure and installation info. Thank you for your time.