Wiring existing 3 Way Switch in basement stairs that was cut
Maybe the reason J Box 1 and J Box 2 were empty is that the previous owner gave up trying to get it to work. If so, this would indicate the problem is in the cables.

If J Box 2 is in a position where a light would be installed, then the circuit was most likely originally intended to be wired like this:



(Put black tape or black paint on the ends of the white wire in the 3-wire cable to indicate that it has been re-purposed as a switched hot.)

If you wire it like this and it doesn't work, then there is probably something wrong with the 3-wire cable, Disconnect everything from the 3-wire and test all the wires for continuity. Make sure all the wire-nut connections are tight - this is where I have the most trouble in my house.