First, in fairness to Jack's Small Engine's, they didn't screw up my order, it was the USPS that took forever. Also, I used ereplacementparts for look-up only, then went to Jack's.
Anywho, thanks for your replies gentlemen.
The fuel bowl (thanks for the theory, Sky) is dry. So, I believe that points to an inoperable fuel pump or an air leak in the pickup tube. (The fuel bowl doesn't have any leaks.) The missing spring cap (I do have a new spring, too.) can't be helping, for sure. Also, I did have the pump parts installed in the correct order. I just didn't realize the cap was missing.
But I think I may have found the culprit: The plastic fuel pipe that I installed came right off in my hand. I'm thinking it was drawing air at that connection. There wasn't enough gas in the tank to cover that connection.
This carb was not fouled badly. The gas smelled "wrong", but no crud at all. I dug in thinking that the disenegrating foam had created obstructions. Before I go too far in this direction (regarding the small balls), I'm going to get the spring cap and a (another) new pick up tube. The brass tube is airtight. When i cover the hole in the carb that it leads to, I can't blow through it.
I think I over did the plastic pipe install. As I noted previously, I heated the brass with a torch, and sat the plastic piece in boiling water. I think the heat fatigued the clamp, as it was on the brass tube when I heated it. Also, the plastic tube seems to have been overheated. What's a good method to install it?