That's what I meant to say under 3) that it could be just an interruption from the telescope antenna to the PCB.
Here's another thing you can try: Let's check if the oscillator is working!
Tune the broken radio to the lowest frequency (87.5MHz) and make sure it is turned on. Now take another FM radio (a small one would be handy) and hold the telescope antenna near the PCB of the broken one (careful, don't touch or shorten anything with the metal rod!). Now tune this test receiver and scan the FM band for a silent carrier (the noise will disappear, like a station without any sound). This signal should be on 87.5MHz+10.7MHz = 98.2MHz on your test receiver. If you found this signal, tune the broken radio a bit higher in frequency - the signal on your test receiver should disappear. You can find this signal again by tuning the test receiver higher by the same frequency like the first one. If the signal in your test receiver does NOT MOVE when you tune the broken radio, that means that your tuning capacitor has an issue and should be replaced or is disconnected from the board somewhere. If you receive NO CARRIER SIGNAL at all, this could mean that the oscillator stopped working OR is tuned to an entirely wrong frequency. If you don't receive the carrier signal around 98.2MHz but way off on another frequency, then again, the oscillator is mis-aligned. NOTE: I think there could be also radios out there that mix the other way around, so if before-mentioned failed, try setting the broken radio to 108 MHz and tune the test receiver to 108-10.7= 97.3MHz where you should receive your silent carrier signal.