My car is a 99 chevy cavalier, 2.4 liter, when it idles it starts to sputter and the engine even starts shaking and every once in a while it dies and is hard to start back up, then when you put it in drive it doesn't go but eventually kicks in a goes, then when you get up to a higher speed and leave it there it is fine until you come to a stop sign and try to go again. The engine light is not on in my car either.

Install a new Ignition Control Module (ICM). This will likely solve your problem. Disconnect the negative battery cable, prior to beginning work.