Getting “Cookies are blocked or not supported by your browser” on login page

Wrangled up some things to check:

@otto via comment on this post

Look at the login page’s HTML source. Is there anything at all before
the initial DOCTYPE line? Even a blank line? If so, then you have some
piece of code creating output before the headers are made, in which
case this prevents it from setting cookies.

Some suggestions from a highly relevant post with several additional ideas on Stack Overflow:

(I know you said that there’s no need to change anything in the wp-config.php file, but references to the old domain could be present. Please verify for sure that this is not necessary.)

Verify the URLs are correct for siteurl and home in the
wp_options table. These can be reset easily by adding the following
to wp-config.php:

define('WP_HOME','http://your-domain.com');
define('WP_SITEURL','http://your-domain.com');

Check wp-config.php for improperly set DOMAIN_CURRENT_SITE constant.

define( 'DOMAIN_CURRENT_SITE', 'yourdomain.com' );

If the W3 Total Cache plugin was/is in use, temporarily remove the plugin from the plugins directory and ensure that the following lines are commented out/removed from wp-config.php:

define('WP_CACHE', true);
define("COOKIE_DOMAIN", "www.domain.com");

Then, remove the following files from the wp-content directory:

w3-total-cache-config.php 
object-cache.php 
advanced-cache.php
db.php