iPhone says to connect to iTunes but computer won't recognize!

I got a broken iPhone 5c from a friend recently and when I had plugged it in and turned it on, it had the Apple Support message and told me to connect to iTunes.

However, when I did plug it into my MacBook Air, it recognized the cord but not the phone. I tried plugging my phone into my laptop and it worked just fine.

I tried going to System Information on my laptop and when I was looking at devices plugged into my Mac, it showed the charger but it did not show the phone, even though it was plugged in.

How can I get this phone up and running? I've always wanted a 5c as well and I'd like to fix it so it works.

What caused this issue anyways?