You need to access your database on the new host and in the WP-Options table, make sure the domain name settings, in the first two rows, are correct. Sometimes, moving domains around, I change those, and then you can’t login – using wp-admin – because it’s redirecting you to the old location.
Also – have you tried accessing either the first installation, on Godaddy, or the Squarespace install, via an IP address?
Did you change your DNS A-record in Godaddy’s domain manager to point to the new location?
Those are all I got ??