Hi,
In Mavericks (OS X 10.9.x) the System Preferences pane that was the Mail, Contacts and Calendars is now the Internet Accounts pane. EDIT On Re-reading I see you were looking in the wrong place.
Just to be really clear:-
The App is called Messages and one of the account (that was added in Mountain Lion) is the iMessages account - which is/was a new service started by Apple for the iPhones and other iOS devices than added (effectively) to iChat to create the Messages app.
However the iMessages account cannot chat to any account that could be used in iChat.
Their ID or Screen Name if you can remember it may give clues.
Older AIM Names tend to be User Name parts of possible longer emails.
Lets say they had AOL as their ISP at one time and their account details would have been Buddy57@AOL.com The AOL service would allow them to use the Aol Instant Messenger service with just the Buddy57 bit.
A Google Mail ID would mean you either used Google yourself or you had Jabber account somewhere that could communicate with other Jabber accounts.
A Facebook.chat ID would have also been a Jabber ID.
Also Apple IDs ending in @mac.com and iCloud issued @me.com and @icloud.com can also be vaild AIM Screen names (generally AIM's own names have no email Suffix (the @AOL.com or sometimes @AIM.com bit) but other people like Apple have aggreeements to use their emails. This includes some ISPs in the United States).
If you only started using the app in Messages in Mountain Lion then it possible that you may have used Yahoo ID (Only ones registered at Yahoo work in iChat 6 or Messages)
The Yahoo option was only added to iChat at the last version in Lion (iChat 6) but is present is the Messages versions since.
If you have managed to sync back your Address Book/Contacts App to your current Hard drive then you may have their details in their Address Card.
Also if you managed to get the Mac User Account info from the Old Drive then your Keychain may also list the accounts you used in the earlier Messages version.
7:55 pm Friday; March 21, 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