Small Engines (Lawn Mowers, etc.): Sears Mower with Honda engine wont start, clutch lever, accelerator cable

Question
Oh what a web I have woven! A few years ago got a sears mower with a Honda 5.5 GCV 160 engine. Trouble started when the transmission lever box (plastic) broke. It was expensive but I ordered the part and replaced it. Seemed Ok for awhile but started to throw the belt. Then it became hard to start so I adjusted the accelerator cable where it clamps on just before it goes to the carb. I found a position where it would run but it still was throwing the belt now and then. I took off the cover on the deck and on inspecting it found the cable for the gear box had slipped out and it was an easy fix to just put it back. I thought finally...but now it won't start. It seems the adjustments I did to make it run when the clutch lever was out have affected it.I tried readjusting the acc cable but dosent help. A spray of carb fluid and it will start - peak - and die. Before I fixed the clutch it was running? I noticed a series of springs-linkage etc for the fuel system so I hesitate to 'fix' it any further. Any suggestions before I take it to a shop? Any help will be appreciated!  

Answer
 Hello Dennis:

 I dont think the Cable Adjustment is the Problem. Try Overhauling the Carb. When you said it was getting Hard to Start; it told me the Varnish from the Fuel was Finally building up inside the Carb. Also it revs up and Quits when you Prime/Starter Fluid the Engine.  Hope this Helps.

 Good Luck

 Respectfully

 John