If you click on an avatar in the chat section, it should load the previous chat discussion you've had with that user (or the initial message that user sent you, if that is the first time there's communication via chat between you two). Not sure why it doesn't complete loading in your case, but chat has been known to behave wonkily.
If a message gets send it will then stay in the chat window. The discussion can be read regardless of whether the other participant is online. Any one side can start a conversation that way.
Also, you should be able to install Barefoot Essentials fine (although it might not solve this particular issue), I am on Windows XP too and am using Firefox and the Greasemonkey plugin.
Thanks for all the detailed answers, I'll try to install greasemonkey and barefoot essentials anyway
EDIT: just installed barefoot essentials, don't see a message from avatar but sent a message and it appears on the right so maybe he started a conservation but didn't send a message, we'll soon solve the mystery