It sounds like you have the default settings, which, in most Windows packages I've seen, usually means that logging as 'root' with password '' is hard-wired into the code and ignores cookies etc. This means it will never offer a log-in window, because it thinks it already has your details, and until you change these settings, uberconversion's answer won't work as the appropriate cookie is never used.
If you got PHPMyAdmin through XAMPP, there's a really easy way to change this at the end of this answer. If not, there are a couple of simple changes needed in config files. There's an answer on superuser.com that explains how to change this - I've included a tidied up answer based on that one here, to save time and in case something bizarre happens (e.g. if it was ever deleted or inaccessible for some crazy reason):
Open the config.inc.php file. Since you are not seeing a log-in screen, you probably have
$cfg['Servers'][$i]['auth_type'] = 'config' in there, probably around line 19. You will also see your name and password. Something like
$cfg['Servers'][$i]['user'] = 'root';
$cfg['Servers'][$i]['password'] = '';
(Recommended) Change the blowfish_secret to any random string. As the file comments say, this string is used to encrypt your password in cookie based authentication (which is what you are about to change to).
$cfg['blowfish_secret'] = 'a rAnd0m str11!11111!11!nG';
Change the authentication type to cookie:
$cfg['Servers'][$i]['auth_type'] = 'cookie'; // DEFAULT: 'config'
(Recommended) Delete or comment out the lines that are storing your password. If, in Priviledges within PHPMyAdmin, the root user has no password, you probably should change that and if the config file says
$cfg['Servers'][$i]['AllowNoPassword'] = true;, probably best to change
false after giving root a password.
If you got PHPMyAdmin as part of XAMPP (ignore this if you didn't), there's an even easier way. Go to localhost/security, follow the link below the table, and it gives you an option to input the password and change to cookie authentification. Note also that XAMPP is funny about passwords - it needs to be less than 16 characters.