Looking at the photos, there appears to be a couple of date labels, 1-06-86, so the thing could be 40 years old.
In that time any of the active components could have been subject a random failure.
Electrolytic capacitors?
Would not be my first suspect.
The quick answer is no, the longer answer is maybe.
Some multimeters can measure capacitance, but to do that the capacitor must be disconnected from the circuit.
One of the failure modes of an electrolytic capacitor is high ESR (Equivalent Series Resistance).
This can be measured with an oscilloscope, but you also need a function generator.
Look here:
If your oscilloscope can display up
Car Shakes to 27MHz, it may be possible to test the transmitter, so giving a better idea of where the fault may be.
JimB