You are just repeating the point that was being argued against.
If the lifetime of the universe isn't enough to randomly produce Shakespeare, 3-4 billions of years are cute but useless to randomly produce anything even near as sophisticated as our 46 chromosome set.
I imagine Dawkins still just repeats the conjecture "but it's 3-4 billion years, anything can happen!"
A work of Shakespeare is a single specific target, that's why it takes so long to hit it - one letter out doesn't cut it. DNA meanwhile is a general purpose animal kit that has many billions of 'correct answers'. It's not about sophistication.
I suggest you read 'the blind watchmaker' by Dawkins to answer your other question.