Lets look at basics you need fuel, air and a spark to fire up any petrol engine I assume you have cheked spark and air if not please do. Now every JD assembly normaly have a fuel in line filter to keep out larger items to prevent blocking the carburator jets. Fuel enters the carburator via a needel valve assembly. It is normaly in this area were problems like fuel starvation starts deu to chemicals settling in this part of the carburator. only fix or cure is to strip and clean. You do get a spray chemical to assist during the clianing process Make shure the needle assembly does not stick after assembly.
Hope this helps
PJ