318 will not start

When it comes to thise carters, if one thing dries up.. the rest is probably needing replaced, carb gaskets, seals, and most importantly for goosing a cold start...the accelerator pump plunger. When that goes, it kills the rpm upon opening the throttle..dead spot and it dies. I bet it just needing an easy carb overhaul.
You can also just raise the idle speed up to help it run for now to prove its faulter, but it seems almost certainly the carburetor is the problem.
Always cracks me up when I see people priming their carbs for cold starts by rapidly pumping the feed pedal. You are probably correct with the diagnosis. A couple quick raps on the carb may fix it all though. Been there more than once but usually on small engines.