I am no expert, but on my model A, in order to engage the back gear TWO separate levers need to be moved, what Boxford call the back gear to the rear left and the ‘sliding gear lever’ on the front of the headstock to the right.

Which lever did you move . The controls also seem to have changed over the years and so more details might help with a more appropriate answer.

Here is a photograph of the plate on my lathe. A/B is the sliding gear lever and C/D is the back gear lever

Is this an old lathe with the motor behind the headstock and visible which is known as the ‘model A’? If it has the motor in the cabinet underneath it is an AUD.

If you have the lever on the front style then with the other lever in the ‘normal’ running position the pulley is released from the big gear (bullwheel). Then you can freely rotate the chuck as it is completely disconnected from the drive. Useful for setting up. However in old lathes sometimes the brass dog inside the headstock that moves bullwheel is too worn or broken to disengage it. So check this first. Later lathes put this lever on the top.

Then the lever on the left moving towards the front engages the backgears, if they are not damaged. If you move the side lever like this but not the front lever then the spindle is locked. Do not use this feature to hold the spindle to apply force to undo a stuck chuck or you will break teh gears. That is a very common problem.

I have a Southbend and I believe that the Boxford is a clone. When engaging backgear, you have to disengage a drive pin on the side of the gear as shown below. The spindle is then driven thru the gears and not directly from the pulleys.

OK so it takes 2 levers. The front one is sort of removing the pin which on the South Bend is linking the pulley to the bullwheel. When disengaged, (lever to left, = pin out) the pulley should rotate freely on the spindle. Look in at the back and you should see the gear moving when you operate the front lever to produce a 1/4 in gap between gear and pulley block. This is where wear or breakage might not move it enough.
Note that there is a small groove looking like a pulley groove at the chuck side of the gear which needs one drip of oil a month and there is a screw at the bottom of one of the pulley block grooves which is an oil hole needing a couple of drips too only when using the backgear. Don’t overdo it to avoid slippy belts but don’t forget or the pully welds to the spindle.

That screw is an oiling point, to be removed and oiled esp. when using back gear, when the spindle and pully rotate at different speeds.

Sounds as if your pulley might have seized on the spindle. Could be bad news. Try oiling generously and rotating each component by hand in opposite directions. Put the front lever in the disengaged position first.