Check the other end of that cable at the switch and see if the white that was tucked away is connected on that end.

I have a similar problem. Main power is coming in at the ceiling fixture, not at one of the 3-way switches, and there are several black and white leads at the fixture junction box. All red leads are lumped with one wire nut. And whites and blacks were also lumped in a certain way. After replacing my old light with new one, I lost track of how it was wired when it was working.
Is there a way to troubleshoot this situation? Presently, somehow I have been able to operate the light with a string-switch at the fixture.
Any suggestions?