Outlook Express stores your mail and account settings to Windows\Profiles\Username\Application Data\Microsoft\Outlook Express.
Note that you might need to enable 'show hidden system files' option before you can access the mail storage in Application Data folder.
You can get the same settings and mails to your new windows by copying the whole OE folder CONTENTS and pasting it over the new computer's profile's appdata/ms/OE folders one.
Make sure you don't copy the new computer to old one though, that would make you lose all your data.