Have you tried the Firetray extension for Thunderbird? https://addons.mozilla.org/en-us/firefox/addon/firetray/
It shows the number of unread emails in the inbox, by marking the tray icon.
I use it in Ubuntu (I prefer kmail in Pardus). However, it doesn't always play that well with the latest builds of Thunderbird, so I have to use an older version of Tbird. That might be difficult to track down for Pardus, I guess.
I can let you know the exact versions I use, if you like? I'd give it a try, and see whether it works for you.