I was able to get it started. So the other alternative is replace fuel lines and perhaps fuel and air filters, maybe run Seafoam through it and hope for the best. I'll try disassembling it tonight.
here's a place to loo for air leaks in the fuel line, where the two lines, upper and lower, are joined by a double barb fitting. also make sure the line is routed thru the space provide, the circular cut out on the left, and is not being pinched. if you smell or see fuel, you'll know you have a bad fuel line.
the K10-WAT rebuild kit contains a needle valve, gaskets, diaphragm, filter screen (below the needle valve) and valve plate. you can start by just replacing diaphragm and gasket (on on the side of the carb with four screws holding the cover) and the one-way valve plate and gasket under the cover that is held down by one screw thru the center. that's where the filter screen is too. replacing the needle valve and lever is the hardest part of a carb rebuild but isn't always necessary. inspect the needle valve and lever. when you press ever so lightly on the lever you should see the needle valve come up about a half a mm. be sure that the valve lever is even with the carb casting where the diaphragm contacts it. inspect the filter screen from the other side of the carburetor after you have removed the one-way valve plate. it should be free from debris or schmutz. there is a replacement filter in the kit. there will be a bunch of gaskets, valves and welch plugs in the kit. most of them are not for your carb. match the ones you use to the old ones.
you'll be working on the weak point of this antique saw, the fuel pump. the carburetor is a long distance from the fuel tank, horizontally but especially vertically and the pump needs to be in very good condition for everything to function. if you see bubbles or voids filled with air in the line, you have one or more leaks. the leaks can be in the fuel line or in the one-way valves in the carb.
here's another picture. print it out if you can and use it as a reference when you're working. note that on the top of the carb the order is: top plate, then gasket, then the one-way valve plate then the carb. on the bottom, from bottom up is the bottom plate, then the diaphragm, the gasket, then the carb. don't screw this up. be sure that the one-way valve plate is aligned perfectly. there are two little locating pins but things can slip and slide while you're assembling. the little "black blob" shown between the one-way valve and the carb is the filter screen. it fits into a cylindrical space below the one-way valve.
work in a clean well lighted place and use a pair of reading glasses that are too strong for you.