Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
The Complete Guide to FaceTime + iMessage: Setup, Use, and Troubleshooting
Troubleshooting FaceTime and iMessage activation
iOS: FaceTime is 'Unable to verify email because it is in use'
Using FaceTime and iMessage behind a firewall
iOS: About Messages
Set up iMessage
iOS 6 and OS X Mountain Lion: Link your phone number and Apple ID for use with FaceTime and iMessage
How to Set Up & Use iMessage on iPhone, iPad, & iPod touch with iOS
Troubleshooting iMessage Issues: Some Useful Tips You Should Try
Setting Up Multiple iOS Devices for iMessage and Facetime
FaceTime and iMessage not accepting Apple ID password
FaceTime, Game Center, Messages: Troubleshooting sign in issues
Unable to use FaceTime and iMessage with my apple ID
How to Block Someone on FaceTime
My Facetime Doesn't Ring
Send an iMessage as a Text Message Instead with a Quick Tap & Hold
To send messages to non-Apple devices, check out the TextFree app https://itunes.apple.com/us/app/text-free-textfree-sms-real/id399355755?mt=8
How to Send SMS from iPad
You can check the status of the FaceTime/iMessage servers at this link.
Have you tried resetting your router? Unplug it from power for about 30 seconds and then plug it in again.
You said that it used to work for you. If this quit working fairly recently and you have a backup from when the apps were working for you, have you tried restoring from a backup that predates the problem?
Thanks Tex and Demo for the attempt.
I just, as in today, received an iPhone 5, and it works on it!
I have tried every link that was pertinent that you listed and reset router. No dice. It just will not connect on my iPad.
My software is up to date, I even tried a new Apple ID with a gmail account and it wouldn't log in, just the same message over and over about my network settings, which work on the iPhone, and my App purchases, and cloud downloads to the phone all work, so...it makes zero sense.
I live in the Caribbean so there aren't any Genius bars here, thus my dilemma
Any further help is greatly appreciated!