New server runs with https
Yes.  How you fix this depends on what you built and what you did.   You did not say if you built a Drupal 6 or 7 site.  It makes a big difference.  You also did not say what mods you made to the settings.php file if any when you uploaded this new site.  

Your 
$base_protocol 
$base_url 

AND a $conf statement as to HTTPS will need to be properly set - depending on which version of Drupal you are using

You may need to modify the DNS zone to accept a wildcard for the domain depending on what kind of site and content it already has and the 

$cookie_domain may need to be properly addressed or Drupal (depending on which one you have ) may drop sessions and log people out by dropping the session if they switch between secures pages classes.  See the issues que of secure pages for examples - and make sure you are looking at the issue that has to do with whichever version you have installed - Drupal 7 and Drupal 6 respond completely differently to SSL and HTTPS issues  See https://www.drupal.org/project/issues/securepages?categories=All

See https://www.drupal.org/https-information for a head start and pointers

As to getting the admin pages to work - usually creating and setting $conf['https'] = FALSE;  should allow http access again by forcing the entire site to non-secure