OK so first of all if you go to http://yourEVServer/EnterpriseVault/
Do you see the page come up at all or do you see it that it couldn't contact the server?
First thing I would try is simply restarting the Enterprise Vault Admin Service (This will restart all your other services like directory, storage, indexing etc) and then run an IISReset to restart IIS
But typically with these things its most likely a directory service/SQL Server issue or a permissions issue
If its the directory service, make sure the Enterprise Vault Directory Services are running, and check the event logs for any 133xx events, such as a 13360 error indicating SQL issues
Check that the databases are online, not in suspect mode or single user mode etc
Also check IIS (Internet Information Services) and ensure the EnterpriseVaultAppPool is running and not stopped.