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Deere found that some Z425 mowers below serial number 060579 have had a common carburetor problem. It seems that the carburetor float needle sticks in the closed position and causes to the engine to starve for fuel. If your mower is below this serial number then there is a new needle valve available from your local Deere dealer that will resolve this issue. The new needle is part number LG690985
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While the carb is still the most likely cause of the problem I'm glad to hear that you have already changed the needle. If your engine runs with the choke on but not with it off then it would indicate that the carb bowl is still not staying full or the main jet is plugged. If you disassemble carb and hold the top half with the float upside down the carb float should sit parallel to the carb mating surface. If your float does not sit level then there may be a problem with the float itself. Old floats were copper or brass and could be adjusted but the newer ones can only be replaced when they wear or deform.
As far as the main jets the newer carbs are very difficult to clean properly. I like to use torch tip cleaners (which consist of a series of different size ribbed wires) to push through the jets in the car. some of the passages are not straight which makes them very difficult to clean. You could also get some carb cleaning dip to soak the carb in for 24 hours. The cleaning dips will dissolve many of the varnish deposits that occur naturally when the engine sits.
Let me know how you make out.