Hi,
If Messages work in either the Guest Account or another Mac User Account but not in your own account the issue is with either the .plists that get stored fro Messages or the Keychain items for same.
Providing the computer is set up properly (DNS Servers, Correct Date and Time in both computer and router, correct region/country in the Messages details button) then the issue Should (i Stress should) be solved by removing the .plist for iMessages (rather than all the ones for Messages as a whole).
Also to be considered in Mavericks is the Read/Write path as well as the final location of the .plists
Because the app is Sandboxed it relies on being passed through ~/Library/Containers/com.apple.ichat/Data/Library/Preferences where Aliases of the .plists point to the final destination. (~/Library/Preferences itself)
This is a view of the ~/Library/Preferences folder using the Modified Column so that both the Containers folder (which is expanded) and the Preferences (highlighted) are in the same shot:-

If you have not worked it out and did not know ~/ is short for Hard drive Name/Users/Your Account name (Little House Icon).
Technically you should have Read and Write permissions on the ~/Library (Home folder /Library) and all it's containing folders.
My Pic shows the Path Bar at the bottom of the window.
You can turn this On in the Finder > View Menu > Show Path Bar.
Lets start with the .plists in the ~/Library/Preferences.
In the Finder > Go Menu > Go to Folder enter ~/Library/Preferences in the Dialogue box to access the Preferences folder (you can Copy it from here and Paste in the dialogue box).
Find com.apple.IMAgent.plist
com.apple.ids.service.com.apple.madrid.plist
and com.apple.imessges.bag.plist.
Do a Get Info on these (Highlight and then either CMD+ i keys together or right click and use the Contextual Menu

In the Panel that opens, scroll to the bottom.
Unlock the Padlock.
Your name should be in the list.
It should have Read and Write Permissions.
Highlight the name.
Using the little cogwheel item at the bottom reveal a Menu about changing the Owner.
If your Name appears but is Greyed Out you already own the file.

After you have checked those three .plist click on the Preferences icon in the Path Bar and Right Click > Get Info

You should have Read and Write permissions and own this Folder.
Repeat the above for the Library itself.
Step 2.
Now use the Finder > Go Menu > Go to Folder to access ~/Library/Containers/com.apple.iChat/Data/Library/Preferences (the upper case C in iChat is important).
You will be faced with a whole bunch of Aliases.
If you click them the Original .plists will be opened (if you have something that can open them)
What you need to do is highlight them and then Show Original option (Right Click)

The window will change but as the two Preferences folder look very similar it can be difficult to check.
You need to only check two in the "containers" route.
com.apple.ichat.plist to check this is "pointing" to the original and the one highlighted in the pic com.apple.imessages.bag.plist
Now you have to use the Path Bar to check all the folders that everything is contained in.
That includes the Preferences folder you are now in, the Library that is in, the Data Folder that contains that and then the Containers folder itself (You should not have to do the Library above that as we checked it above).
Step 3 will be the Keychain but I will wait to hear on this first.

8:15 pm Wednesday; July 30, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad