Well, the internal operation between the power lead and the remote turn on is in effect the same as a relay (small current controls larger...)
So if the fault is in the amp, and it stays always on, a relay on the +12V line, controlled by the remote turn on wire should work fine - just get a relay capable of handling the current the amp demands. Normal automotive relays are typically capable of 30A, though I've seen 20A and 40A as well.

You might want to connect the other (functional) amps remote turn on terminal to the switched terminal of the relay, so that the relay is the only thing powered by the remote turn on lead. If the relay doesn't come with a diode across the coil, consider installing one (1N400x diode should be fine), or some other protection.

/Michael