There's the right answer, and the real world answer.
The right answer is that they should've warned you about any other issues there may have been following the original repair, and the fact they didn't and that it's now more broken means they should take responsibility for that.
The real world answer caveats that with the fact they may technically be right, and that they did do what you asked them to (replace the cracked screen, I assume) and you could've dropped it again after you picked it up. Did you test it in front of them in the shop? Was that even an option? You could argue in court that you deserve a refund if the screen has been fitted incorrectly, but there's no guarantee that you'd win as I suspect they'll bluff their way through with technobabble and leave you nowhere to go. I would, if I were them.
Take it somewhere else, see what they say and if it's fixable, and then get it done there. Write the other lot off as a bad experience and tell as many folks as you can, IF it's proven it was their fault. I suspect they get a lot of people coming back in with these 'issues' that have developed again, so they're just arguing their corner to avoid being taken advantage of.
It's not the answer you want to hear, but if I'm honest I don't think I'd waste my time arguing it. Maybe go back in once more, be really nice and then if they still don't budge stand outside all day and show/tell everyone who walks in what they did