I am assuming that what you are saying is that you cannot pull the rope out like the engine is tuck.
If this is the case, there is a very good likleyhood that the engine has locked up and will need to be replaced. Since you did not tell me if it was a 2 cycle or a 4-cycle engine, I will give a few reasons for each as to why the engine may have locked uo.
Some are correctable some are not.
Both Two Cycle: And 4-cycle
1. The engine may be locked by what is known as a Hydro-lock. This is caused by
a carburetor that is overflowing and filling the cylinder with gas or gas oil mixture. On a 4-cycle it can also fill the oil pan with gas and thin the oil and push the oil into the cylinder. In this case, the carburetor must be cleaned and rebuilt with a complete carburetor rebuild kit. (Or a new carburetor) Remove the spark plug and try to turn the engine over. Be careful as you may push fuel out the plug hole.
2.. The electric starter gear may be stuck on the flywheel causing the engine to lock up.
This can be corrected by removing the cover and dislodging the gear from the
Flywheel or removing the starter and repairing the gear assembly.
3. There might be a stick or rock stuck in the auger causing it to lock up. Clear any ovstructions form the auger.
4. A belt may have come off of the pulleys and loged between the pulley and the frame of the engine.. Check and replace belt.
1. Accidently using fuel that did not have the proper oil mixed in the gas.
2. The use of 87 octane (Regular) gasoline. All two-cycle engines must use primium gas or it will ruin the engine. It scores the piston and cylinder through detonationand overheating.
3. Using old gasoline left over from last year. This causes gum and varnish to form on the piston and cylinder and stick them together...ruining the engine.
4. A broken connecting rod inside the engine.
1. Running the engine with low or no oil in it will lock up and ruin the engine. Replace engine.
2. A broken connecting rod or other internal part. Replace engine.
Before you follow the following suggestion, Make sure you check the spark to make sure you have spark. If you do then follow these instructions.
The most likely cause of your problem is carburetion.
This accounts for about 90% of all snow thrower repairs. Snowthrowers are not used very often and they tend to have the gas left in them for longer periods of time than it should. Gasoline cannot be used if older than 30 days.
As engines sit or get older, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems. Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
Today's gasolines contain MTBE and alcohol. (Ethanol) They turn to "Junk and garbage" very quickly. Alcohol is partially water (H2O). And they call it "Oxygenated fuels! It is the oxygen that breaks down the organic compounds in the fuel and turns the gas to "Garbage" (Gum and varnish) The fuels we had just a few years ago had no alcohol in it and would store for longer periods of time before going stale... and fuel stabilizers do almost nothing to prevent the fuel from going bad with the changes in today's fuels
Do not buy gas from the "Discount" Stations. The discount stations get a reduced price on gas because they may be buying fuel that is nearly 30 days old already. You may be getting fuel that's nearly stale right from the pump when buying from a discount station. Purchase your fuel from the well-known stations such as Shell, BP, Sonoco, Phillips 66 etc.
More than 70% of all of our repairs in our lawn mower business are due to this same issue. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carburetor.
The carburetor must be removed from the engine. Clean all parts with carburetor cleaner and blow out all the small holes and passageways with compressed air. Remove all of the non-metallic parts since the carburetor cleaner will cause them to be disfigured decompose and plug the carburetor as time goes on.
Wash the carburetor cleaner off of the metal parts by washing them in warm, soapy water then rinsing with clean water. Dry them by blowing it off with compressed air. Make sure that all the passageways are blown dry before reassembling.
Reassemble using a NEW carburetor rebuild kit.
DO NOT TRY TO REASSEMBLE WITHOUT USING A COMPLTE CARBURETOR KIT! You will just end up having to do the job again.
ALWAYS clean the fuel tank and replace the fuel line when doing this repair or you may have to do it all over again. The inside of the fuel line disintegrates over time and these small pieces of rubber will plug up the carburetor too. Dirt and water from a dirty fuel tank will also plug up the carburetor. Find the Model, type and serial or code numbers off of the engine and take them to your local dealer to get the carburetor repair kit.
If you do the work yourself, take pictures or at least make a drawing of where all the linkages, gaskets, and component parts go. Correct reassembly is critical.
If the carburetor still doesn't work correctly, you may have to take it to someone who has an "Ultra-sonic" cleaning machine. This machine uses carb cleaner and ultrasonic vibrations to get the very small passageways clean when traditional methods fail.
If you don't feel comfortable with this kind of repair I would suggest sending it to a reputable shop.