Hi,
If...
An AOL account check that the Messages > Preferences > Accounts lists it without the @aol.com ending.
I gained my AIM name years ago whilst using Netscape in OS 9
It is listed in System Preferences > Internet Accounts as the ScreenName@AOL.com but in message is is just ScreenName
If...
It is an Apple issues ID (@mac.com, @me.com linked to iCloud or and @iCloud.com one) then make sure the password is 16 characters or Less.
Technically if you started wit @mac.com and have upgraded as Apple have change to MobileMe then iCloud you may have all three types of ID that might be linked to the same Email and Apple ID account.
However in Messages they can be used as three Different Screen names.
This is not the case in iChat where older versions do not do the double login to AIM and Apple that allows the password to be used.
If you are getting "Disconnected" Showing is there a ~ type/lightening type icon next to it ?
If there is what does it say if you click on it ?
The Server name should be api.oscar.aol.com
The port should be 443 (but 5190 will work as well)
SSL should be used.
Avoid Proxies if you can and use the System ones if you cannot.
IF you have an AIM or AOL name (they can be issued from either even though they are the same company) try Logging in here https://settings.aim.com/
This may tell you your account has been suspended.
This can happen if you travel out of country (unusual use) particularly if another device is still logged in at home.
9:10 pm Tuesday; April 21, 2015
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