Small Engines (Lawn Mowers, etc.): Carburetor problem, air fuel mixture, briggs and stratton

Question
I got a mower from my mom that sat dormant for a few years outside.  I took it apart and found water mixed in the reservoir of the carburetor with the gas.  It was all thick with white chunks.  I cleaned it some and put new gas in but I don't think the gas is getting to the engine when I prime it.  I squirted gas directly through the spark plug hole and got a momentary spark, so I think the only problem is with the fuel getting there.  I noticed the was a bulb like that in a toilet that is supposed to move freely up and down but it sticks because of the buildup.  Is there a part can get for this or use some type of cleaning solution?  It is a Yardman 20" MTD with a Briggs and Stratton engine.  Thanks.

Answer
 Hello Steve:

 If you want to do it Right , then Here we go. If the Carb Doesnt have a Fuel Shut Off Located in the Bowl. Read my Directions that I have Written and Decide if You Want to Attempt this Repair. I Will Be Here to Assist if you Need Me. A Repair Shop is My Suggestion Because of the Cleaning Solution Involved. If You Follow the Instructions on the Cleaning Solution, You Can Perform this Repair. The Carb is going to Need an OVERNITE SOAK in Carb Cleaner. It Sounds Like a Heavy Coating of Varnish From the Gas is Built up inside the Carb, so Spray Cleaner Isnt Going to do the Job. I have seen it at the Local NAPA, but Im Not Sure about the Price. The Carb Should Sit in a Vat (completely covered by the Cleaning Solution) for at Least 24 Hrs. Be Careful if you Do this Yourself. **Use Rubber Gloves When Working with this Cleaning Solution.** Then ALL Ports and Passages Blown Out with Compressed Air.**Dont Forget to Wear Safety Glasses** Replace all Old Parts and then Set the Carb Air/Fuel Mixture Screws (if your carb has them) at 2 Turns Out From Seat. If the Carb wasnt Too Gummed Up with the Varnish that the Gas Formed, then the Engine will Start. When you get to this Point and the Engine is Running then Let me know and we can Fine Tune the Carb Settings. Hope this Helps. Let me know what you Decide, Please.

 Good Luck  

 Respectfully

 John