Hey
I've had the same problem and my network provider was very helpful in helping me fix the problem. For those like me who need step by step instructions, i've listed them below, it may not apply to some cases
Go to settings ==> connectivity ==> phone
scroll down to network where the network selection button is. Now, in my case, it is automatically connected to my network.
Click 'Network Selection' button and select manual, which will prompt you to select your service prover. Click a provider that is not your own. An error will come up and close settings.
Turn your phone off then on again, and check network is selected back with your service provider.
Skype then signed in no problem