How to restore backup from old iPhone onto new iPhone?

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I have an iPhone 5s which I dropped in the toilet, so ATT sent me a new one and I'm trying to transfer everything to my new iPhone. Fortunately my old phone was mostly still working and I was able to back everything up onto my Mac. I got my new phone and went through the prompts and connected it to iTunes. It shows at the top like it is syncing but then won't do anything else. The screen continues to say "connected to iTunes" and when I disconnect from iTunes it tells me "connect to iTunes."

I can't manually go to devices and select restore from backup because it's shaded in gray. I feel like there is probably some simple explanation but I'm so lost and frustrated. And of course I had 10 days to do this and waited until the last day.

If I go to the ATT store can they just transfer everything for me?

Thanks so much in advance! I'm obviously not very tech savvy.