Question: Why is the Terminator able to talk when he looks like a human but doesn't talk when he doesn't have the living tissue on?
Answer: While it's subject to whether you count it as canon or not, the recent anime "Terminator: Zero" confirms Terminators can still speak even if they've been reduced to their metal endoskeleton (though the anime makes a point of showing how eerie it looks since the Terminator just lets its jaw hang open while words come out in a distorted, mechanical pitch), so presumably it indeed was a case of either the T-800's voice parts getting damaged by the tanker explosion or it just had nothing worth saying to the two people it was trying to kill.
Answer: Think about what produces sound coming from human mouth: air directed through the tissues of the neck and mouth, moving vocal cords in waves. After being burned, there is no tissue which can create the waves when being moved.
Chosen answer: It's not that he could not talk, but perhaps he just had nothing to say. Once his skin burns off, he was still in pursuit mode to terminate his target. Before the skin burned off and he was chasing them in that scene, he wasn't saying anything either. And it's also logical to say that the wreck and gas tanker exploding, which caused his skin to burn off, likely could have damages internal components of the terminator by impact force as well as the extreme heat. So him not talking was either he didn't have anything to say, his voice generator was broken, or both.
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