Since your ISP says everything is okay, it may be possible that this is the result of a virus or corruption on your machine itself.
Outlook Express stores your emails in files with the extension "pst". If a virus or other malware arrived in your inbox via email, it could be that the pst file was harmed, thus the problem with your inbox.
Otherwise, you may be able to access your pst files to find your old email.
Just in case this is a malware issue, I'd recommend scanning your machine to see if anything is still actively causing a problem.
MalwareBytes is pretty good for this, as is AVG Free and SpyBot: Search and Destroy. Best case scenario: there is some malware on there, and cleaning it out solves the problem automatically.
There are ways to access the pst files, and even import the old email into your new Outlook, but first I'd recommend just trying to clean any existing malware out, and see if the easy solution works.