I cannot send/receive messages on my iPad. Nor will it let me sign in…or out.

Re: iPad messages: "Nor will it let me sign in…or out"

Wondering if you are getting an error message that may help,

or if you have tried turning messages "off" and back "on" again.

Restarting your device can sometimes help restore order if something is not working:

How to: Restart your iPad - Apple Support

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Re: "FaceTime is doing the same thing".

1. 1. Open Settings.
   2. Tap FaceTime, then tap Use your Apple ID for FaceTime.
   3. Sign in with your Apple ID.

For more info. see: Use FaceTime with your iPhone or iPad - Apple Support

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If either app still doesn't sign in successfully, try these solutions in Apple Support's article for Mac and iPad.:

See what to do: If you can't turn on or sign in to Messages and FaceTime when you try on your Mac or iPad

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Re: "I cannot send/receive messages on my iPad."

Apple support have another article online that may help:

You can choose which issue you are experiencing and follow the steps.

(Eg: You can scroll to: "If you receive messages on one device but not the other")

See: If you can't send or receive messages on your iPhone or iPad - Apple Support

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More info. / support / contact options etc. (online chat / phone / email etc.)

Messages Support website: Messages for iPhone, iPad, Apple Watch, and Mac - Official Apple Support

FaceTime support website: FaceTime - Official Apple Support