Try this. Put the .dbx files wherever you want to permanently keep them on your hard drive. I would create a folder outside of My Documents, but that's up to you. Open OE and go to Tools, Options, Maintenance, and click on the Store Folder button. Click on Change, and change that to the folder where your .dbx files are located. Click OK and close out of OE. Open OE again and see if your messages now appear in Inbox.
By the way, in your old computer, did you add folders in OE, or were you only using the standard Inbox, Outbox, Sent Items, etc.?
