Messenger and Skype now use the same backend. Therefore people still on the Messenger network and on the Skype network can chat seamlessly with each other. However, the Windows Live Messenger CLIENT has been discontinued.
The "Messaging" Hub on Windows Phone, Windows 8, Outlook.com and Xbox still works as usual since it's the same backend.
When you login to Skype, you need to click "Microsoft account" and then login with your Messenger username and password (Hopefully they change this soon, so you don't have to click that first).
You should then see all your Messenger contacts there. You'll need to merge accounts if you don't see your past Skype contacts there.
If you're unable to login to the Messaging hub on your Windows Phone anymore, there may be an issue with your account or your phone, since it should still work perfectly fine.
Also, since you said 90% of your contacts are there, it could be an issue with them as well. But really, it all should work perfectly fine as long as you are using your Microsoft account still and not a separate Skype account.
Hope this helps