we have a 20055 that I just overhauled. It was taking 12 primes and two pulls to start cold. Had good compression, etc., just had 20 years of use on it. I cleaned the carb - very simple carb, replaced the o-ring that the carb sits up against, the plastic intake tube, gaskets, and replaced the primer base. It starts first pull now again with only the three primes shown on the sticker. Some later models have an auto choke. Although the diagram will probably show both, ours did not have the auto choke. You either have the auto choke or the primer model. My guess is that the combination of the O-ring maybe leaking a little, and the base maybe leaking a little kept ours from starting first pull. The valves were tight too. Since Toro numbers are usually sequential, your 20043 is probably older than ours. If you are looking for lowest cost fix, try replacing the O-ring the carb sits up against, checking the base gasket to see if it shows an even impression. If it does, replace the gasket. If it does not then replace the base too or use two gaskets. Might check the valves too but be sure you are 1/4" past TDC. I had ours there and must have bumped it just a smidge, and ground too much off a new valve. Had to buy a second one and wait a week. When I looked at what I had done, it was only a 1/8" or so off where the piston should have been to set it. It was hardly noticeable but the cam lobe was already in a spot where it had a few thousands lift in it. Kicked myself because as a former automotive machinist, no way should I have made that oops.
