I am not trying to say it would be conscious without being run. [...] I am trying to say that the computation as an abstract function has an output which is the sentence "I believe I am conscious."

Now I think I agree with you. (Because I think you're using "output" here in the counterfactual sense.)

But now these claims are too weak to invalidate what trist is saying. If we all agree that l-zombies, being the analogue of the calculator that's never switched on, never actually say anything (just as the calculator never actually calculates anything), then someone who's speaking can't be an l-zombie (just as a calculator that's telling us 6 + 9 = 15 must be switched on).