Just an update to the seeming hopelessness of this situation.
I have an iPhone 5s with iOS 7, an iPad 2 with iOS 7 and an iMac with Mavericks (OS X 10.9.5).
All three of these have sent and received all messages for a year now. Suddenly, on Sept. 9, it all broke. My Phone continues to work fine, but the other two will not receive nor will they send. (I am only trying to send to other Apple devices).
Several times I have logged out and in again from iMessage, even reseting my Network settings on the iPad per one suggestion. Nothing.
Again, I just now logged out of iMessage and FaceTime on all 3 devices, then back in again starting with m y iPhone. As I logged on thru my iPad, my iPhone received notices saying that the iPad had connected to my account. Then when I logged on thru my iMac, both my iPhone and my iPad received notices saying that the Mac had connected to my account.
So it is clear that they are connecting to the server in some fashion, but still not sending nor receiving of iMessages. )FaceTime does work though).
The only thing out of the ordinary that I did was to partition my drive on the Mac and install the Yosemite Beta. I logged into my account on Yosemite, used it briefly and then closed it, rebooted to Mavericks and continued on. I did not realize that the problem with iMessage had started until several days later when I looked at my iPad and noticed a few messages had failed.
Could logging into my Apple ID thru Yosemite have screwed this all up? (Incidentally I did NOT start using iCloud Drive was I know that would have broken things in the cloud).
I hope that someone who reads these posts will have an idea about what we can do.
Thank you.