I just flew from New York JFK (where cellular reception on the ground is a bit spotty) and used the onboard Fly-Fi to access the internet at the gate and during taxi. Once we were airborne I couldn't get my phone to connect. I'm a software engineer and a former technical support person (as is my husband) and neither of us could find any trickery to get my phone to connect.
I found a thread over on Flyertalk where a user (ostensibly a JetBlue employee) is reporting that this is currently a known issue. Until a fix is posted, it's probably best to use Fly-Fi only after you've taken off.
With my phone now unable to access the internet, I grabbed the laptop out of my bag and it worked fine. Until I tried to access my Google account:
Yup, I'd recently enabled 2-factor authentication and now couldn't receive the text I needed to access it! So the second lesson here is: make sure you set up new devices on the ground before you leave if you have 2-factor authentication enabled.
(From what I understand, I probably could have gotten around the bug if I'd had a MAC-address spoofer on my phone, but I don't...)