Google 'POP3' and have a read of how it works. Looks like you've been leaving mails on the server. The ones you've deleted on your desktop were only copies that were downloaded to your desktop.
Renaming the inbox file will not change the situation as OE will create a new one, and will start downloading the same 1900 e-mails again.
See if you can change to an IMAP mailbox, that should give better results with setups such as these.