Ok, the databases are there and the SQL sever is accessing them.
Can AC run on the server?
Is AC showing up on the control panel\programs and features, can you repair it?
Could you do an old backup of the server or a partial to get AC back?
Did you send AC any money, if so it should be easy to get a new license number and reinstall.
Marc was right about the export function but it takes a long time and make sure you have enough space. Ed was right about an external program may be faster
