[Arran]

According to the schematic I have the BC antenna coil is labeled as part #2, they call it a transformer on the parts list, this is in addition to the loop antenna. The pushbutton bank has coils but they are switched into the BC band oscillator circuit when part #17, the BC and Police oscillator coil is switched out. There must be a position on the band switch for pushbutton tuning, if the bandswitch is on standard broadcast the pushbuttons will not work, if the bandswitch is on pushbutton the dial tuning will not work. It's possible that the BC oscillator coil might be open, or burned out, I would check the primary and secondary with your ohm meter, the primary is lugs 1, 2, and 3, secondary is 4, 5, 6 and 7.
Regards
Arran