The cord pulls but doesn't trun the motor?

need to open it up and check the springs and the bars for wear or damage

could be the pawl catch on the crank shaft is not working properly, if this is an easy start model, there are two springs and two pulleys to inspect. usually second spring is the problem.

the little conter wieghts have catch tabs to engage a hub. sticking springs are causing this problem spray some wd40 or similair blow gun and clean the entire assemble

There are starter pawls that catch the flywheel when the rope is pulled. They are plastic. You will need to disassemble the unit and remove the starter assembly to inspect the pawls.

Possibly the recoil starter pawl's on the inside of the recoil housing not engagning with the flywheel.

I have had this situation before on a lawnmower. I didn't have a craftsman, but is probably the same issue. Basically, the spring that recoils the cord back in either broke or came unwound. When the mower is not running, the cogs on the pull chord keeps the cord from coming out. When the mower is running, the spring is not wound enough to hold the chord in and thus releases or doesn't hold it in.
Try pulling the pull chord assembly off and rewind the spring.

The procedure for starting an engine is as follows:

• Check that you have the throttle in the start position and/or on high revs with choke on
  
• Prime the engine by pushing the button about 5 times
• Pull out the cord until you meet resistance. Then let the cord go fully back into the engine and then pull the cord out sharply. Repeat this until the engine starts but not more than a few times.
• If the engine doesn't start, try pressing the primer button another few times then try to pull start the engine
• If the engine doesn't start after a few pulls it may have flooded so leave it for a few minutes before pulling the starter rope
  

you need to pull your spark plug and check that cylinder is not hydrolocked with fuel or oil first, then with plug out see if it will pull the motor over or pull out any farther than it did before. If everything is good there, I would check underneath the deck and see if you can spin the blade by hand,(make sure your spark plug is still out for safety) next I would pull the rewind top off motor and visually inspect the Flywheel and coil gap and look for something possibly binding or catching on the flywheel, I think that model has a flywheel brake, maybe that is not adj. correct.....good luck hope I gave you some ideas, If by chance the cylinder is full of gas..replace needle and seat in carb.

Hello, W/D here.

Most of the recoil starters have ball bearings in them, and the centrifugal force that you apply pushes the balls out where they engage pawls and allow the flywheel to be rotated. Since your's is on a snowblower, you may just be stuck, or moisture could be in the mechanism, freezing the ball bearings in place.
The quickest thing to try: Rap the recoil mechanism in the middle of the top, with a rubber hammer. You want to jolt it, without denting it. Try to pull the cord and see if it engages. You can repeat this several times, but try not to dent it.
If the machine is outside, and you believe that the mechanism may have frozen, you can apply heat to it with a hair dryer, and then rap and try.
Try these out and repost if the problem persists.
Best regards, W/D

dry the plug asmall squirt of aerostart in the top of carbywith air cleaner off full throttle pull the rope and she should fire up make sure the on/off switch is in the correct position. no don`t laugh ican remember nearly completely stripping amotor years ago before ichecked it put it all back together and it started first go try the aerostart and switch