if you're using a control panel like cPanel/WHM, there is an option to transfer accounts to another server.
no other DNS or SQL ..etc configuration, just one click and your website will be live on the new server.
change the domain nameserver to the new server.
if suspended, you may be able to contact the datacenter or the provider to give you access to download your data. if terminated i guess you could not get them back.
Get in touch with your server provider, and see what happens