Moving to new host

If you closed your account with godaddy then they probably terminated the account and that would mean, no you can not access your dashboard. You should contact your new host and say you cant import a .sql file and they will help you. You should be able to import a .sql, I would find it extremely strange if there was a host out there that would not let you do that. The other thing you mentioned about not being able to upload to the new server is also something I would ask them about. All your problems are with the new host, not the old one.

If you already pointed your domain name to the new host then using it will not go to your godaddy website anymore. Since WordPress bases everything off of the domain name it would be difficult to use the dashboard on a web space that does not have the domain your database has in it. I think the best way to solve this problem is call to new host and say “why cant I upload files and why cant I import my .sql file.” if you were able to do those 2 things and you are using the same domain name your site will work exactly how you had it.

If you have control over your domain as in you have control over the “Name Servers” then yes you can point your domain to anywhere you want. Keep in mind it can take a long time sometimes for the domain to register to which site is being pointed to so this can result in a long process. I think up to 48 hours in some cases, I have always experienced it happening in a just a couple of minutes.