You seem to use pop3 for your hotmail account, the emails have been downloaded to your computer, and they are no longer on the server since you unchecked the option "leave a copy of messages on the server." You can also use http for your hotmail account, the http account works directly on the server, so it should be possible to put back the emails to the server. I tested it with Windows Live Mail, here are the steps:

1. Setup both pop3 and http account for hotmail.

2. Drag emails in pop3 account to http account.

3. Sync http account. Emails were copied back to the server.

But when I tested step 2 in Outlook, I always got the following error message:

I don't know how to solve this.

Hope this gives you some hints.