Download the Opera Mail installer, launch it, click "options", set "install path" to a folder on your desktop, set "install for" to "Standalone Installation (USB)" and install. In that Opera, set up the mail account fresh (do not import and do not uncheck "leave messages on server").

Does it work in there? If so, we can try to figure out what's wrong with your normal install.

Or, first, log the connection and see what the log says.