Chris obviously didn't read the question fully and missed you where using outlook express, the mails are stored in several folders and are .DBX files for outlook express.
On the old machine, the easiest way to locate Outlook Express' email store is to ask Outlook Express itself. Fire it up, and then in Tools, Options, on the Maintenance tab there's a button labeled Store Folder. Click that and it will tell you the folder containing your email folder.
Browse to the location of that folder (you may have to change the view options in folder options to show hidden files and folders) Copy the entire contents of that directory to a floppy, CD-ROM, or a usb pen drive.
Now Fire up Outlook Express on the new machine, and Select File, Import, Messages.... Choose Microsoft Outlook Express 6 and press Next. Select Import mail from an OE6 store directory and press Next. Now on the next screen, browse to the location that you've placed the message store we saved from your old machine. (CD or pen drive) Import, and your messages should now be transferred.
if you want to do the address book then use you import and export on the file menu to export the address book on the old machine and import it on the new machine.