iChat can join the AIM Service or the Jabber set up (And Yahoo in iChat 6)
AIM refer to their "Names" as Screen Names. Jabber ones tend to be referred to as IDs.
When Apple created iChat in 2001 they "did a Deal" with AIM to have the IDs registered and issued by Apple recognised as Valid AIM names.
At that time that was the .Mac (dot mac) service's @mac.com ending names.
The Trial accounts and Lapsed accounts as well as paid for account remain Valid Screen Names.
Apple then changed to MobileMe and issued @me.com names
Only Paid for Accounts worked as Valid Screen Names (well this time Trial accounts only worked while they were on Trial)
Other Apple IDs (i.e. other (email) names that you may have used to create an Apple ID) are not Valid AIM.
MobileMe will end completely on June 30th.
Currently new Apple Issued IDs are the iCloud ones (Also using @me.com)
Now unfortunately there are now degress of @me.com names.
Those issued by iCloud only work in iChat 6 (In Lion) as that version also logs in to Me.com and this allows the AIM Servers to "read" the password.
It means iCloud IDs will not work in iChat 5 or Earlier.
You can still register for @mac.com names here
Keep the Password to 16 characters or Less (AIM Server limit)
You cannot create a new Apple ID using the email linked or in use as another Apple ID.
Apple IDs created using an external (to Apple) tend not to be valid AIM Screen Names unless they have been Registered at AIM's registration
At AIM you can create your own name (Only the bit in front of the @ gets used) or register an "outside" email (where the whole ID is used.)
You can use any Email to create as many AIM IDs as you want.
Jabber IDs come a variety of spread out and separate Jabber servers.
These servers that are what is called Federated to allow contact between one server and another meaning you can use Jabber IDs from another server from the one you use in your Buddy list.
Google with GoogleTalk allow people with Googlemail IDs to use their Email as a Jabber ID (They run a Jabber server)
Facebook also run a Jabber server.
Although Jabber IDs are in the form of NameYouCreate@theJabberServerName.com they are rarely email addresses as well (Google are the exception and Facebook look like they are going the same way).
There are thousands of Jabber servers around the world.
Registration is rarely On line via a Browser and has to be done though a Jabber App that has the Registration Module (this can find Jabber server and list them for you)
iChat does not have this registration Module.
You may not have an Apple ID of the right type.
It may be the right type but has expired if it is MobileMe (you tend to be able to Login in here and the iTunes Store but cannot do much else including purchases at the store).
Your may have an ID that has a password that is too long.
You may have an iCloud ID and an older version of iChat that will not work together.
You may have a "name" or ID that is valid with iChat. (this will depend on which Service your potential Buddies use)
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously