From the Settings App, try checking the Skype settings. Once you are there, touch the "Notifications" button and it will display on-off buttons for Sounds and Alerts. If they are off, turn them on.
Yes, I am getting rings when someone calls. Not sure what else might be the problem there with your installation. So far, that's all I know that might affect the ringing in Skype. I know that the iPad 2 has some wierd behavior with the mute switch so that even if you turn up the volume, if the mute switch is set you still won't get rings.
you might have mute on. It only affects alerts and system sounds.
If you has the switch above the volume buttons set to Mute, check that. If it is set to orientation lock, double tap to get the Multitask bar, swipe from left to right, and check the mute button there.
This tip helped me
I had the exact same problem but I think I have found the solution.
Goto your ipad settings, Settings>Notifications
Make sure you have "Skype" under In notification Center. If it shows up under the "Not In Notification center", Simply click on the "Skype" icon, and turn on the "Notification Center". I chose alert style of "Alerts" Also make sure that you have "Sounds" turned on. That's it and Now it rings when someone calls me on skype on ipad!