The iChat has become Messages, in newer OS X this acts a bit different than former iChat. There had been a transition some time ago, and even the dot Mac situation is also different. Seems to me it no longer worked a year or so ago; accounts in .mac had some grace period, the details are fuzzy because I never had an AIM, .mac, or iChat, etc account.
The connection of .mac to the mobileme days made some mac.com names for iChat, or so I heard. Lapsed account names using residual mobileme or .mac account names from the time were still allowed. Some related details, not an answer to your question, appear in an ASC discussion from last year:
•iChat stopped working... (May 2013)
https://discussions.apple.com/thread/5072761?answerId=22139588022#22139588022
For a variety of iChat and .mac results, links, see:
https://www.google.com/search?q=.mac+support+iChat
There is an older support article in those results that may be worth a look.
However the iChat application may been the best thing to have used, once you sort the details; and when set up on the other end, hopefully it would just work and you won't be called upon often to figure out where they went wrong using it.
Not sure what web-based alternative would provide instant message capability in Leopard 10.5.8; however for a time, Google accounts let their members use some message service online. There had been changes there as some things were discontinued without notice; other items were google+ only.
The need for an external iSight (FW400) camera with the eMac for video support to Chat is another detail. I have an external iSight in a box, never used though it should function. Once set up, it would be adequate in the last model eMac, if you happened across one.
An old version AIM for download, perhaps possible to help setup? some antique iChat, was noted at oldapps. Be wary of other items that may follow on some software download sites, such as genieo, & adware... http://www.oldapps.com/mac/aim.php?system=mac_os_x_10.5_leopard_powerpc
Sounds like a project to me.
Good luck 🙂