“La llamaría, pero no contesta.”

Question

“La llamaría, pero no contesta.” Hola, I’m confused. I would/should/could call her but she doesn’t answer. If he called and she didn’t answer it seems “La llamé, pero no contesta” makes more sense. Muchas gracias, Shirley.

Answer

I think the idea is that he had already called her in the past and is speculating about what would happen if he called her again in the future.

Answer

Hola Shirley
It's a bit difficult to see, I agree, but it is what Marcos is suggesting. By reading the previous sentences and what comes after it is as if they've tried to call her before with no luck so she now know that if she called again she won't answer. Maybe if we added a bit more to the sentence, this idea would be clearer:
La llamaría [de nuevo], pero (ya lo he intentado y) no contesta. 
I hope this helps.
Un saludo
Inma