Just to follow up, I shut off the petcock, removed and cleaned all the lines, and found it still wouldn't start. I replaced the gas pump itself at this point, because we'd had a problem with the old gasket under the glass bowl previously - no vaccuum. It fired right up with the new pump.
I'm still pretty sure I've got a bunch of junk in the tank, but at least now I know what to do about cleaning the lines, etc.
Thanks!
- rick