A common problem that I run across with Tecumseh engines that run, but then don't after I remove the carb bowl is that the bowl gasket is cracked. Sometimes I can actually see some fuel come out of the seal, sometimes I don't. It seems to seal just fine until the bowl is removed and then never seals right again in some cases. In other cases, I've flipped the gasket upside down from how it was installed first, making sure to install it on the carb first, not the bowl to make sure it doesn't fold into the bowl and it will seal again.
I would remove the spark plug and give it a few pulls too just to make sure water didn't get down into the cylinder via the intake manifold, that could cause other problems.