After downloading my Yahoo mails to Thunderbird, the mails on the
server are deleted!!

Although I have full access over my emails from yahoo account through
Thunderbird, I just want my emails to be back on the server because I
am about to format my computer...

Anyone know how to do it?

unchecked the TOOL>>Account Settings>>Server Setting "Leave Message On server". 

>>And what happens when Uncheck " Untill I delete or move from
Inbox".Which inbox it is refering
>>to Webmail or TB account.

That would mean deleting the message from your Tbird Inbox. Tbird
would then delete the mail from the server.

A step by step description of the solution is available here
http://helpdesk.graniteschools.org/docs/Document.asp?ID=226

~~~~~~~~~~~~~~~~~~~~~~~~~
When you check your mail in Thunderbird, it deletes the messages off
of the mail server as it puts them into the Inbox in Thunderbird.  The
downloaded messages are then accessible only from that computer.  If
you work at two locations, you can change the incoming mail server
settings so that Thunderbird leaves the messages on the mail server so
that you can download them at both computers.

   1. In Thunderbird, from the Tools menu, click on Account Settings.
   2. On the left, click on Server Settings.
      'Server Settings' screen
   3. In the Server Settings section on the right, check the Leave
messages on server box.
   4. If you check the For at most ... days box, Thunderbird will
delete the message off of the server after the set number of days.
   5. Check the Until I delete or move them from the Inbox box.
   6. Click OK.
   7. Repeat these steps on the other computer where you want to
download your mail.  You should now be able to download your messages
on both computers, as long as you do not move the messages from the
Inbox or delete them.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

i have the same problem, and these comments are very useful for
stopping more emails being deleted from the server, but does anyone
know how to return the ones which have already been moved?