You guys were right. The moral of the story... make sure the fuel tank is clean.
I disconnected the inlet line at the pump and used a vacuum pump to make sure I was getting fuel out of the tank, and I was. There was a little sediment coming through the line, but the line was not blocked.
I took the pump off and took it apart, and it had a lot of sediment in it. I cleaned it as best I could, tried to flush the check valves, and reinstalled it. Still no fuel, so I replaced the pump.
I installed a clear filter ahead of the new pump, and flushed the pump-to-carb line. I got A LOT of crud out of that line. I suspect either that line was totally plugged, or the pump check valves were not sealing, or some combination of both.
So, cleaning or replacing the tank is on the top of the to-do list. I'll also replace the lines. That'll give me peace of mind knowing I've got a completely new fuel system.
Thank you all for the advice.