Sir Mo Ma . . .
With your final submission of the model number of your unit, there is now no ambiguity of it being confused as being one of the smaller "Coke bottle " units, with your unit being a "cooler" unit, as is being shown at the very-very end of this post.
Plus your units case is large enough to be incorporating full blown " All American Five " superhet circuitry within its case.
Plus it has a full loop antenna installed within its back cover . . . .it interwinds about 2 inches of the the loop winding within two separate gaps in the masonite back . . .those two areas being plainly visible.
ADDITIONALLY there is a Fahnestock clip nearby which will accept an additional long wire aerial connection, however, the loop antenna itself should provide a myriad of stations being received.
Pending . . . . . that you are not sited at Amboy crater out in the Mojave desert.
Now . . . .investigating your suspicion of a defective osillator coil.
Initially confirm this fact . . . . via schematic referencing . . . that the osc coil is consisting of four connections.
the main windinf that is resdonating in conjunctio wit the osc tuning condenser section, with there being a tap off on this coils lower portion.
Now the main point of interest would be the fourth "comnnection" of the osc coil terminals, with the schematic showing it as being an open swirl of loops, but being open of electrical connection at its very end .
And that is exactly how it is physically, composed of a number of turns of wire interwound with the actual oscillator coil windings.
Sooooo . . . this connection, in actuality is serving as a "gimmick" capacitance with its low capacitance intercoupling, replacing the usual ~47pf silver mica coupler that couples back into the osc tubes circuitry.
The 3 connections should ohm out inter-continuity, while the gimmick winding would show an open circuit connection.
Tests to really-really detect for an oscillator presence:
Use a battery powered digital meter and stab its + test lead into the cathode connection of the osc tube and its - lead going to the 1st grid of the osc tube. A properly functioning oscillator will then give you a negative voltage reading of several volts usually minus 4 ------minus six. That varying with set circuit design, along with the extreme end of the band that you are being tuned to.
An other testing procedure is to put another set belly to belly / back to back with your set and depend upon the new test set as being your aural monitor for oscillator activity of your "Coke" set.
Since your "Coke" set will be capable of receiving AM band signals from ~550-1700 Khz its local oscillator will then be operating from ~ 1005-2155 Khz in receiving that spectrum.
Therefore if the monitoring receiver is then tuned into a "quiet" spot above ~ 1005 Khz it can "listen" in as the "Coke" set is slowly tuned across the band.
HOWEVER, that signal presence is NOT going to show up as a rumbling freight train, in actuality, showing up as a very subtle hum , which is easily overlooked by a novices initial trial of this procedure.
A very MARKEDLY better procedure is to tune the monitor receiver to pick up a weak station within that given spectral range and then further off tune the reception to one side of the station, until the sets audio is then still feebly distinguishable.
If the "Coke" set is then tuned across the band, instead of the freight train rumble, you then will receive its whistle as a heterodyne "birdie" which is initially being at a high frequency, that gradually decreases in frequency to Zero and then again rising as you tune past.
( A complete aural comparison is akin to the sound effect used in movies of a bomb being dropped to ground . . . and then . . . AND THEN . . . . the bomb reversing and making a return path BACK up to the bomb bay door.)
This lets you know that there is an oscillator presence on your "Coke" set.
Thassssit . . . . .
73's de Edd