Update loop

I apologize if this has been answered but it takes so long to explain that I’m not sure how to search for it.

My site is moving to a new server and thus I need to move my blog. I downloaded and installed the latest version of WordPress to the new server, and uploaded the backup of the previous database. I ended up having to do this again, since I needed to change the address of my blog. Once I did that with my new address, however…

1. I can LOOK at my old weblog, but cannot access the admin menu. Going to wp-admin points me to the login page for the NEW weblog.

2. The new weblog loaded the title and description of my blog… and nothing else. None of the posts were copied over.

3. When I go to login to the new weblog… I am told that I need to upgrade my version of WordPress. The new blog is running on the newest version of WordPress, so upgrading is impossible!

If anyone could help me with this seemingly endless loop of nonsense, I would appreciate it.