The pull cord on your Weed Eater is an integral part of a two-cycle engine's starting system. In order to start the engine, the cord needs to adequately get the flywheel and crankshaft spinning. If the cord gets stuck or won't spin the flywheel smoothly, the flywheel won't spin fast enough to generate magnetic energy and discharge the coil's spark. Disassemble the starter assembly to determine why the pull cord won't spin.
Underneath the starter cover, the cord is housed in the groove of a pulley. This pulley spins when you pull the rope. It is connected to the flywheel. If the pulley cannot spin along the starter post, the flywheel won't spin either. A cracked or bent pulley flange will stop the rope from moving. The starter post -- which the pulley rides along -- also needs sufficient lubrication to spin. Re-grease the post with an all-purpose engine grease. Take the cord out of the pulley and clean the pulley with a mild soap, such as dishwashing liquid, and check for sticky spots or cracks. Replace a damaged pulley.
Broken Recoil Spring
Inside the pulley, a recoil spring is attached. When you pull the cord out, you stretch the spring, and when you let go, the spring snaps the cord back onto the pulley. This spring can bend and break if you tug too hard on the cord while starting. Overstretched springs require replacement. Check the hook on the front end of the spring to determine if it will connect to the pulley. When reinstalling the pulley, make sure the recoil spring is connecting to the pulley, which should give it tension.
Sheared Flywheel Key
The flywheel rides along the crankshaft stub and is connected to that stub through a thin metal part known as the flywheel key. If you hit the head hard against a rock or a curb, or drop the motor while it is running, you can bend the flywheel key. If your key is bent, the cord won't pull out in short bursts or possibly at all. If the recoil spring, pulley and cord are all fine but the cord is still stuck, you'll need to remove the flywheel and check the key.
The crankcase houses the crankshaft. If there's too much pressure or not enough pressure inside the engine, the crankshaft won't spin and neither will your pull cord. This usually happens when the piston in the cylinder has seized up either from overheating, from too much friction, from dust in the cylinder or because of any of the three combined. This generally means the engine's shot, as buffing down a piston or replacing it often exceeds the cost of a replacement trimmer.