I'm having the same problem as many others, and I'm getting pretty frustrated with Windows 10 overall (starting to really miss Windows 7).
I'm using a desktop computer, so obviously I have no use for airplane mode. yet the operating system forces the feature on me, and now I can't turn it off. When I slide it to off, it pops right back over to on.
I've looked at all the solutions thus far (press Fn + F2, Fn + PrintScrn, etc.). Nothing works. If I boot into safe mode with networking, I can indeed access the Internet. However, when I boot normally, no luck; airplane mode is stuck on. I've tried a selective startup and eliminated all the nonessential startup items; still no luck. My computer is now worthless from a business perspective because I can't access the Internet or my home network (no email, no nothing) -- all because of a feature that has no place in a desktop environment in the first place.
Microsoft, I really don't need a stock answer ("Go to settings," etc.). I need a solution. And fast.