Can't access one of my WP sites anymore

The site is live, the login page is working but when I enter my password it says that password is unknown (WP site). Then I try to reset my pw but it says email address is not recognized, what the heck.

So I login to phpMyAdmin, select the right database, change my e-mail address there, change my password as well after converting it to MD5 code, and I try to login again and still nothing.

I try the "lost password" function again and this time I do receive the pw reset email (as I changed my email address inside the database already), so I follow the link, reset my password, try to login again and again password failure, I try it another 5-10 times in case I make spelling errors too often or anything but no way to be able to login, all the time the same message.

What I suspect what can have to do with it is this.

When I type in site.com/wp-admin I get redirected to:

hxxp://www.site.com/wp-login.php?redirect_to=hxxp%3A%2F%2Fsite.com%2Fwp-admin%2F&reauth=1
But there are no www redirections in my cpanel, but it is possible that I changed it inside the WP dashboard some day.

Any idea how or where to fix that inside the database?