I have moved my test site to the live server.

But there are config files with urls that need to be updated so nothing would work.

I uninstalled JMS on my test site and uploaded this to the live server and then re-installed JMS. But now I cannot login to frontend or backend. If I rename /multisites to /multisites_ then I can login.

I do not get incorrect login or similar error message, I just get the standard page refreshed. Is there more config files (or session files or cookie making files) that need to be addressed?

If you shared the users between websites and move your test environment on a live environment with another domain name, then you may have problem to login in the website when you are not on the same.

If you are using Joomla 1.5 and sharing the users, to get access on your master website that has shared users with another domain name, you can temporarly update the /multisites/config_multisites.php to put in comment the section that declare the cookie domain for the master website

define( 'MULTISITES_MASTER_COOKIE_DOMAINS', '.DOMAIN.COM');

When working on Joomla 1.6 or 1.7, you can update the "configuration.php" file present in your master to clear the "cookie_domain"

Once you will get access to your master website, go in JMS manage site and open/resave any slave site.
When it is sucessfull saved, this rebuild the cookie domain information for the website.
Perhaps you will also have to update the domain declared of the slave site to reflect the new domain and deploy folder.