Test that the light is good in a different socket
Poke the pins in the socket with a plastic rod, or an electrician's screwdriver, if they are both springy the socket is almost certainly good.
Turn the breaker off conform that it is off using your non-contact voltage detactor. This is what they are good for, it is pretty much all they are good for.
You've already experienced the flaws with non contact voltage testers.... they are not accurate. Get a good multi meter from your home store.
Make sure you check for any GFCI's outlets that might be feeding the light. They might have tripped.
Start testing from the socket and work your way toward the source. Look for your voltage between the switched hot and ...