On the webmail is there any way you can mark the mail as unread?
The other alternative is to download them to another pc (If you have access to a friends maybe) then export them to a pst file then import them into your Outlook.
I am not sure if this will work but you could also try deleting your mail profile within Outlook (or setting up another with a different profile name) then reconfiguring it and then do a send / recieve. It may download them again into the new profile.