In no special order, the Silence destroyed the TARDIS, they and Kavorian broke away from the church under the impression that the Doctor was piloting the TARDIS when it exploded. And no, we never did find out who's voice it was that River heard in the TARDIS.
But the silence alone couldn't destroy the TARDIS. They had to tell someone to do it. I suspect it was River as she was the one trapped onboard. So she died twice.. Once there and once in the Library..
I used to think it was River, and maybe it was. She
was the one trained and programmed by Kovarian in the first place.
When the Kovarian Chapter breaks away from Trenzalore, they don't just go shooting at the TARDIS until it explodes. The Doctor wouldn't be stopped that way. No, they set up the Silence on Earth. They set the stage at Demon's Run to abduct Amy and her baby. Eventually that baby grows up to be Mels, who tries to kill the Doctor.
I like to think that River still had some subconscious "kill Doctor" things in her brain. It's very possible that she attempted to destroy the TARDIS in "Pandorica/Big Bang" without even knowing she did it.