Someone may have a more elegant solution, but here's several ways I know of:
If you have not set up your new system, you can back up the place where your old emails are stored, copy them to the new system, and then tell the new system where to look for them. On your old system, under OPTIONS, look to see where your personal storage folder is located (this might be under the MAINTENANCE tab). That's the file you want to back up. On the new system, find out where your personal storage fold is located, and overwrite it with the one from your old system.
Another option: Set up a second "indentity" on the new system, and copy the old personal storage folder there, and then use the import feature to import the messages from one identity to another,
Finally: You can save the individual messages you want to keep as separate files. Hilite the message and do File | Save As and give it a name. Save them to a CD, and then on your new system, drag'n'drop them into your Outlook Express mail bin.
Hope this helps, if you have questions or need more precise guidance, let me know. This would be much easier in Outlook!