The first thing I’d do is to dump (erase) cookies in my browser.
However, I’m not sure whether you really deleted everything and started from scratch, what data you deleted (the database?), or whether you simply reinstalled WP over the original installation. It sounds like the latter, since your “blog was still there”.
Initial solution (especially if you’re using Internet Explorer): dump cookies and empty cache, then try to visit the blog again.
I use Firefox and Mozilla on Linux. I have indeed deleted cookies.
I have deleted the database several times but I can still see the original blog posts, plus some others which have appeared following attempts to reinstall. These were partially successful but when I tried to log in I got a message saying I needed to upgrade my database. (Perhaps because of a couple of error messages.)
Present position is that I set up a new blog on the WP host. I will gradually transfer at least the more important material and will provide a link to the old blog as well, assuming other people can see it (can you?) – http://www.acampbell.org.uk/blog.
I wish I understood what was happening. I suspect something may have changed on the server although t he admin people deny this.