Hi,
Lets be clear.
If you only have an iMessages account active in Messages on the Mac you will not see if the Account is On line or not.
The Status Item in the drop down Menu is a hold over from when the App was iChat and works only when an Account that has a Buddy list (even if not displayed) is Enabled (Bonjour, Aim, Jabber, Yahoo).
As everyone has the Bonjour Account you can enable this for the Status item to change the Status (not that it effects the iMessages account at all).
IF the Messages Menu > Preferences item is also greyed out and you cannot access anything you have an issue with the AppleGothic.ttf Font.
Open the Font Book.
Scroll to the bottom of the List (several Apple ones are here).
Highlight the AppleGothic one and use the File Menu > Validate
Also make sure it is not duplicated (or if it is that one is Turned Off).
At this point restart the Mac.
If this does not solve the issue navigate to Hard Drive Name/Library/Fonts
Highlight the Font and then use the Duplicate option in the Finder's File Menu.
Delete the original and change the Duplicates name to the original name.
10:02 pm Friday; August 1, 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