[Radioroslyn]

OK Turn the set off. Measure the resistance from the wiper (the wire that goes to the coil ) to the chassis with the volume full up. Should see a low resistance like a few ohms. If it is much higher like several thousand ohms then your primary on the coil is bad (open) or you have a bad ground connection where the primary winding this ground to the chassis.
If the coil is open...
That part of the coil is somewhat noncritical in terms of it's inductance as it's used transferring or coupling the rf signal to the secondary which is a tuned circuit. Take the coil out and this winding will be the small one near the bottom. Rewind with suitable ga magnet wire. You can guess or approximate by counting them. The phasing or direction doesn't matter on this winding.
If the coil measures a low resistance..,
Then you have a bad ground connection at the volume control or a dirty control.
Me I'm betting on the open coil. It's easier to troubleshoot w/the coil disconnected from the pot as their resistances interact. Also you didn't say whether you where measured the pot, across the pot or from the chassis to the terminal on the pot. This adds another factor into the equation

GL