Outlook Express doesn't store e-mails individually. Instead, it packs them all together in a single file for each folder (Inbox, Deleted Items, etc). It seems that some of these files may have been corrupt. Fortunately, Outlook Express automatically re-creates any missing folders; you can make use of this to correct the problem.
Firstly, ensure that there's nothing in your Inbox which you want to keep. (If there is, simply create another folder (e.g. 'Saved Mail') and copy the mail items to there.
Close Outlook Express and run a search for *.dbx
This will show each of your OE 'folders' (which are, in fact, single files). Right-click on 'Inbox' and select 'Delete'.
Restart your PC (I'm not sure that's absolutely necessary but I always do it anyway!), then open Outlook Express. The software will spot that the Inbox is empty and automatically create a new (empty) one. Hopefully, that should fix the problem.
Chris