I had a problem with Incredimail & after a lot of trouble searching the registry trying to delete it all, I reverted back to Outlook. I didn't lose any emails, as far as I know emails are held solely by the ISP & programs like Incredimail are just tools to go & fetch it.
You would still have most e-mails left on the server if your e-mail reader is configured to leave a copy on the server when read, but if not, they get wiped as soon as you read them. I have been using incredmail for quite a while now and haven't had any real problems. As Woody suggests back up the mail files under incredimail and restore when you have incredimail working properly.
I know this dosen't help you with your problem, but I had so many problems with Incredimail, I deinstaled it and went back to Outlook Express. my biggest problem was replying to Emails, it just would not send them. I could send mail ok, but not Relpy.