You say "All outlets show 110v with a circuit tester, but fail to power a known good drop light with a 100w bulb".
What type of tester are you using?
Are you removing the outlet plate and testing the wires or using a plug in tester?
If you are testing the wires going to the outlet and they show 110v, and you plug in the drop light and it does not work, it is probably a bad outlet and it feeds the other outlet so neither one works.
Charlie O.