Unable to log into iMessage and intermittent issues with FaceTime

Question

Late 2011 MacBook Pro, OS X 10.8.4.  I'm an admin level Windows guy but a relatively new (and otherwise very pleased) convert to Mac OS.
This morning Messages started repeatedly prompting me for my iMessage password and FaceTime has starting working only intermittently.  Both work fine from my iPad and iPhone 5.  Both have been working from my MacBook Pro for months.
This morning when I tried to fire up Messages on the MacBook I got an error saying "The server encountered an error processing registration".  After doing some Googling, I noticed that many folks said that when they had this problem they also had an issue with FaceTime.  I confirmed that FaceTime was indeed giving me the same error as iMessage. After trying some solutions from past threads that didn't work, I rebooted.  Now instead of throwing an error, Messages just keeps asking me for my iMessage password again and again.  FaceTime works occasionally but sometimes when I get a call and click answer, I get "call failed" as my iPhone and iPad continue to ring and then I'm asked to re-enter my password on the MacBook.  If I enter my password it just sits and spins.  If i quit FaceTime and start it again, it'll usually log in successfully but calls may or may not work (following the same pattern I just mentioned).
The odd thing to me is that when I tested FaceTime on my iPad, I got notifications on my iPad and iPhone and my primary and alternate email address were now registered with FaceTime.  They have been for over a year so I'm not sure why I'm getting those notifications again.
I'm able to log into the Mac App store without a problem using the same AppleID
What I've tried so far based on Google results:
1. In Keychain Access, reset my default keychain - No improvement
2. In Keychain Access, selected Keychain First Aid, repaired and verified - No improvement
3. On my iPad, turned iMessage off and back on - No improvement, though iMessage on the iPad still works fine
4. Confirmed that my primary and secondary AppleID email addresses and password are correct.  The email address associated with my AppleID is not associated with any other AppleIDs.
Thanks!

Answer 1

This could be a complicated problem to solve, as there are many possible causes for it. Test after taking each of the following steps that you haven't already tried. Back up all data before making any changes.
Before proceeding, test on another network, if possible. That could be a public Wi-Fi hotspot, if your computer is portable, or a cellular network if you have a mobile device that can share its Internet connection. If you find that iMessage works on the other network, the problem is in your network or at your ISP, not in your computer.
Step 1
Check the status of the service. If the service is down, wait tor it to come back up. There may be a localized outage, even if the status indicator is green.
Step 2
Restart your broadband device and your router, if different. You may have to skip this step if you don't control those devices.
Step 3
From the menu bar, select
 ▹ About This Mac
Below the "OS X" legend in the window that opens, the OS version appears. Click the version line twice to display the serial number. If the number is missing or obviously invalid, take the machine to an Apple Store or other authorized service center to have the problem corrected.
Step 4
Take the steps suggested in this support article. If you don't understand some of the steps or can't carry them out, ask for guidance.
Step 5
From the menu bar, select
 ▹ System Preferences ▹ Network
If the preference pane is locked, click the lock icon in the lower left corner and enter your password to unlock it. Then click the Advanced button and select the Proxies tab. If the box marked SOCKS Proxy is checked, uncheck it. You don’t need to change any other settings in the window. Click OK and then Apply. Test.
The result may be that you can't connect to the Internet at all. Revert the change if that happens, or if iMessage still doesn't work. Remember that you must Apply any changes you make in the preference pane before they take effect.
Step 6
Select from the menu bar
 ▹ System Preferences… ▹ Flash Player ▹ Storage
and click
Block all sites from storing information on this computer
Close the preference pane.
Step 7
Enable guest logins* and log in as Guest. Don't use the Safari-only “Guest User” login created by “Find My Mac.”
While logged in as Guest, you won’t have access to any of your personal files or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
Test while logged in as Guest. After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
*Note: If you’ve activated “Find My Mac” or FileVault, then you can’t enable the Guest account. The “Guest User” login created by “Find My Mac” is not the same. Create a new account in which to test, and delete it, including its home folder, after testing.
If iMessage worked in the guest account, stop here and post your results.
Step 8
Boot in safe mode and log in. Note: If FileVault is enabled on some models, or if a firmware password is set, or if the boot volume is a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to boot and run than normal, and some things won’t work at all, including Wi-Fi on certain iMacs.  The next normal boot may also be somewhat slow.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. After testing, reboot as usual (i.e., not in safe mode) and test again.
If iMessage worked in safe mode, but didn't work when you booted out of safe mode, stop here and post your results.
Step 9
Reset the NVRAM.
Step 10
Reinstall OS X.
Step 11
If none of the above steps resolves the issue, make a "Genius" appointment at an Apple Store, or contact Apple Support.