After hundreds of starts, the nylon pull cord is showing signs of wear and tear. This most often occurs at the handle, or at the wire spool. Either way, nothing a new piece of nylon cord can't fix. The T-handle at the end of the pull cord is most likely the removable type. If this is the case, nylon cord from any hardware store will suffice to get the mower back in action.
Disconnect the spark plug to make sure you don't accidentally start the mower. It may be necessary to remove the spark plug in order to get the cover off the lawn mower engine. The cover houses the pull cord reel and return-spring assembly.
Remove the engine cover using a Phillips-head screwdriver. Put the screws in a jar or an old cup so they will be handy during reassembly. After removing the screws, slide the cover off the engine and turn it over. Set it on a clean flat surface.
Pull the old cord out as if starting the engine. Once the cord is fully extended, lock the pull-cord spool in place with a pair of vice grips. The pull cord fits in a notch in the spool and is held in place with a knot tied in the end. Cut the knot off, but do not pull the cord out. The old cord will help fish the new cord into place.
Remove the T-handle from the old cord by prying the top out of it with a flat-head screwdriver. Removing the top of the handle reveals another knot within the handle. Cut the cord below the handle and set the handle aside.
Measure the length of the old cord to determine the appropriate length of the replacement. Cut the new cord to length. Butt the end of the new cord to the end of the old cord that was cut from the handle. Tape the two pieces together with a couple of wraps of electrical tape. Don't use too many wraps, as the tape must fit through the guide hole into the cover and pull-cord spool.
Reach into the cord spool and pull the old cord out from the inside. This will pull the new cord through the guide and into the spool as the old cord is removed. With the new cord installed, remove the electrical tape and discard the old pull cord. Tie a knot in the end of the new cord inside the spool, then place the cord into the notch.
Slip the other end of the new cord into the T-handle and allow several inches to stick out the top. Tie a knot in the very end of the cord and pull it down, back into the handle. Reassemble the handle. Remove the vice grips from the spool and allow the spool to reel the new pull cord onto it.
Replace the engine cover on the lawn mower engine and secure it in place with the screws. Reconnect the spark plug and give the pull cord a try.