HT201270 I have done all of this but still get the 'no service' signal. Can anyone help with this?

Question

Carrier settings updates are small files (about 10 kb) that are installed on your iPhone or iPad (Wi-Fi + Cellular models). Carrier settings include updates to Access Point Names (APNs), MMS settings, features such as tethering, and default apps such as Stocks, Maps, and Weather. You might receive notifications periodically about installing a carrier-settings update.
Follow these instructions to update your carrier settings:
Make sure your device is connected to the Internet.
Tap Settings > General > About. If an update is available, a prompt will appear.
If your iPhone is using iOS 4 or earlier, follow these instructions:
Make sure you have a working Internet connection on your computer.
Download and install the latest version of iTunes.
Connect the iOS device to your computer and open iTunes.
Select the device on the left side of the iTunes window and click Check for Updates. If a carrier settings update is available, iTunes displays a prompt.
Restart your device.
Note: Occasionally a carrier may release a mandatory update. This type of update will display only an OK button instead of an Update button, to let you know that the update was downloaded and installed.
If you need to know the version of the carrier settings your device has, tap Settings > General > About and look next to "Carrier".

Answer 1

I did the verification, which indicated that the last backup was 0422 today.  However, when I opened my Mac, this morning at 0500, I still got the message that the backup was NOT performed, etc, etc. etc.
The backup is made on the standard Tiime Machine.
The next backup has already started as of 0518.  Let's see what happens.  This is strange.  Here is the time sequence: 0518    Backup started
                0525     Mac. froze and color wheel would not allow me to access anything on the Mac,
                0528     Backup continuted:  91.9 MB of 94.8 MB
                0530     92.2 MB of 94.8 MB
                0532     Backup stopped.  Message: Latest backup 4:22 Today.
It seems to be functioning properly at this point.  I'm curious to see if I get the standard "The backkup was not performed because an error occured while copying files to the backup disk" message, later today.
I appreciate your help.  I'll keep you posted as I may need your help again. 
Thanks