Login loop in 3.6 with multisite

I have a problem with logging in after setting up multsite in 3.6.
I have set up several multisite installations with previous versions of WordPress, some on newly purchased domains and hosting and some replacing static sites, and I have never run into this problem.

I did a manual install of WP 3.6, not going through the cPanel, because i like to customize table prefixes, etc.
Everything worked just fine.
I set the permalinks, disabled all plugins (there were only two – Akismet and Hello Dolly; I didn’t see Jetpack anywhere?).
I added define( 'WP_ALLOW_MULTISITE', true ); to my config.php and uploaded it by FTP.
As expected,I saw the Network Setup appear in the Tools.
I clicked and got into the Network setup, where I carefully copied and pasted the code into my config.php file and my .htaccess file and uploaded them (after saving copies of the originals).
I clicked on the link to login again and the familiar login page showed up.

That’s when the problem occurs.
When I input my username and password, it just reloads the login page again.

I have tried changing my password using the “forgot password” link, same thing happens.
I have tried changing my password in phpMyAdmin, same result.

I’ve called my hosting tech support and they are as stymied as I am – I have scoured these forums and Googled my fingers to the bone, and I’ve tried several different things, but can’t find a way to fix this.

I have deleted everything, created a new database and done a clean install, so at least I have access to one site, but I really want to create a second site and need network access to do so.

I’m not sure a link to my site will help, since it’s just the basic install with no content and no working plugins, but just in case, it’s at http://alphamare.ca

Can anyone help me out here?