CA3080s are fragile and fussy about the current fed into their Iabc pin (modulation pin, pin 5). If that gets over about 1ma, they die. This circuit seems to be relying on using PNP Q5 to limit that current and modulate it with a variable amount of voltage fed into the depth pot on Q5's base. If some situation fed current into the control or Q5, it could kill the 3080.
To test, turn the amp on, no signal. Measure the voltage between pin 4 (-15V) and pin 5. If that's zero or more than about 0.7V, the 3080 is dead. Internal to the chip there is effectively a transistor base-emitter between pin 5 and pin 4. If it doesn't measure like a single base-emitter when powered, the 3080 can't work.
Ordinarily I'd expect the 100K in the emitter circuit of Q5 to limit current to the 3080, but I can see some situations that would feed too much current in there.
If the 3080 pin 5 measures OK, there may be something else messed up with the bias circuit for the 3080. Test it by lifting the collector wire of Q5 to the 3080 pin 5, and subbing in an ordinary diode from the lifted collector wire to -15. Now measure the voltage across the diode that is faking the pin 5 to pin 4 diode. This should stay between zero and 0.7V for all possible settings of speed and depth pots. You should be able to see a variable LFO signal across the wiper to ground of the depth pot, and also from +15V to the emitter of Q5. If that's not true, there is a fault in the circuitry between the LFO opamp and the depth pot.