In our basement there is a small room we use as a pantry. We put a screw-in receptacle where a light bulb would go and plugged in a fluorescent shop light. The wall switch is blocked by a refrigerator. So for 20 years we have left the switch on and turned the light on and off by the pull string switch. It stopped working. I took it down, replaced the bulbs, plugged it in a wall outlet to make sure the new bulbs worked and everything was fine. I put it back in the pantry, plugged it in and it still would not work. I have replaced the ceiling fixture and the wall switch and it still does not work. A non-contact detector indicates there is power all the way to the fixture. All the other lights on the breaker with this switch work fine. What am I missing?
Ever use air tools? The air pressure line comes from the compressor, goes to the tool, and where does the air go after that? it just disappears, into the magical aether, or really, just the air.
Ever use hydraulic tools? The hydraulic line comes from the pump, through the tool, and then there's a second hydraulic line back to the pump. Why? So you don't flood the shop with hydraulic fluid!
Electricity does not work like a compressor where the power comes out the hot and just disappears into the aether (except in Australia, where it does, but nevermind that).
Actually, electricity works like hydraulics, except it's two-way, so the return line is just as important as the supply. That return line is where your problem lies. This is called the neutral wire.
Measuring the neutral wire with your voltage tester may be useful. It should read no voltage. If you measure hot voltage there (with the light on), the problem is between there and the breaker.