Following steps have helped many of our user to come out of such weird state. you may give it a try:
Go to sync.opera.com
Login to your account using same username and password
you will find an option to "reset synchronization" there
When you reset synchronization, you won't loose any data from device.
Once you reset synchronization, logging in to your device
Tap on the red Opera icon at the bottom right (may be a different place if you are on tablet mode), go to settings and there will be the VPN for you to enable it.