It sounds like your carburetor needs cleaning. A good way to check that this is the problem is to put about a teaspoon of gas into the throat of the carburetor and then try to start the motor. If the motor starts for a second and then dies this indicates that your carburetor is dirty.
There is also a gasket between the air filter plate and the carburetor body which may need replacing. Do you know the model, type and code number of the motor? It sounds like it is a Briggs and Stratton engine. The numbers should be stamped into the blower housing either right above the spark plug or above the muffler.
We'll try the easy way first. This way you won't have to mess with governor linkages and rpm settings.
Okay, here is what you do. You will need a spray can of carb cleaner. When using carburetor cleaner remember to ALWAYS wear safety glasses. Cleaner in the eye can be very painful at best and life threatening (Yes, LIFE THREATENING) at the worst.!! (And using spray cleaner it is very easy to have spray back into your eyes).
Remove the spark plug. Remove the air filter and the air filter housing (should be two screws attaching it to the carb throat).
Use some small vise grips or something to pinch off the fuel supply from the tank and then remove the bolt from the bottom of the carburetor bowl. Carefully remove the bowl from the carb body being careful not to knock or damage the plastic float. Let the float gently drop down and hang from its hinge.
Carefully remove the rubber o-ring which seals the edge of the carb bowl. Check it for cracks. Take a look in the bottom of the carb bowl. If there is any green sludge or any deposit, spray it with carb cleaner and rub it away with a rag.
Now, using the "straw" attachment which should have come with your carb cleaner can, spray cleaner up the centre tube in the carb body. Spray the cleaner up under the rest of the carb body. Follow this with a GENTLE blast of compressed air if you have it, to dry the cleaner up. Hold the float gently while you are using the air so that you don't damage the hinge of the float or blow the needle inlet valve away.
Look down the throat of the carb from the spot where the air filter housing attaches to the carb. You should be able to see 2 or 3 small holes facing you. Again, using the straw attachment, spray the cleaner into each of these holes. Put the straw right up to or into the holes. Spray into these holes and you should see the cleaner start to drip out from underneath the body of the carb where the float is attached. When you see the cleaner start to drip out then you know these passages are open. Follow this with a gentle blast of air.
Now carefully replace the o-ring around the carb body which seals the carb bowl. Make sure it is not twisted or kinked. Being careful of the float, replace the bowl onto the carb and re-attach the bolt to hold it on. Spray a little bit of cleaner down the carb throat around the throttle butterfly which is at the other end of the carburetor. Make sure the butterfly valve is moving freely.
Take a good look at the gasket between the air filter housing and the carb body. This particular gasket is very easy to tear. Make sure the primer hole is unobstructed by the gasket and that it will line up correctly with the hole in the carburetor. If there is any question about the gasket, replace it. A new one will be a couple of bucks.
Re-attach your air filter housing and air filter. Make sure the air filter is clean or new. Re-install your spark plug. Add fresh from the gas station fuel. Do not use boat gas or marked farm gas in your small engines. Check the oil level is correct. Prime the motor and then pull it over. Now what happens? Has that fixed the problem?
Please let me know how it goes. If that doesn't solve the problem then we can re-assess your situation. If it has solved the problem for you, please click on the green Accept button. Good luck.
Sorry to be late getting back to you. I didn't realise you had replied.
It's good that your primer is now working. However, it sounds like your carburetor is still plugged.
You can remove the entire carburetor from the motor by removing the bolts behind the carb and pulling it toward you. Once the bolts are removed the carb will slip off the intake manifold tube. Make sure you don't lose the o-ring and plastic ring which seals the carb to the intake manifold. Be sure to draw a diagram or take a photo of the throttle and governor linkage on the top of the carburetor before you remove it so that you can hook it back up when you replace the carb.
After you remove the carb have a good look up underneath the body of the carb without the bowl. Make sure that all the holes you can see are clear and clean. There is a tiny hole in the throat of the carb on the left hand side as you look at it from the air filter side. Make sure this passage is open by spraying cleaner through it. The fluid should drip from underneath when you spray into this hole. If it seems blocked you can try to dislodge any grunge by using a VERY small wire. It will have to be tiny. You don't want to enlarge the hole in any way by forcing a too big wire through. Don't push too hard as you don't want to break the wire off in the hole. Look up the main nozzle which is the tube which goes from the inside of the bowl to the centre of the throat. Make sure this is all clean. There may be a tiny o-ring up there. If you can see it, make sure it is seated properly. Spray carb cleaner into the throat from the engine side of the carb. There will be 2 or 3 pin prick size holes on the side of the throat near the throttle plate. Make sure you get the cleaner in these. If there are any adjustment screws on the outside of the top of the carb remove these and spray carb cleaner into the holes. Follow with air and replace the screws. Do not screw them in tightly. Just screw them in gently until you feel the screw stop. Then turn them back out about 1 1/2 turns.
Take a look at the intake manifold tube. Make sure the tube is securely attached by trying to gently wiggle it back and forth. If the tube is plastic then check it carefully for cracks. The plastic ones have a habit of breaking right up where it attaches to the engine block.
Re-attach the carb and hook up your throttle and governor linkages. Make sure the gas in the tank is fresh from the gas station. Gas only has a shelf life of about 1 month unless stabilizer is added. After that the octane level drops and there isn't enough Oomph to allow for proper burning.
Let me know how you go on. Hopefully this will work for you. If not then I would say that the carb probably needs a soak in some carb cleaner solution to remove some stubborn deposit that isn't coming out any other way.
Let me know how you go on.
I hope you receive this posting. I asked them powers that be to re-open the question.