a transitory way to connect to vcenter could be an entry in file /etc/hosts in your PC/MAC...
what is the version of vCenter?
check if vCenter services are running?
Check log files for any errors.
have you tried to login using VI Client?
Check if your local systems DNS IPs are correct.
Changing the hostname of vCenter 6 or PSC 6 is not supported.
Thanks for the replies.
I've managed to get the backup server online (I'd forgotten about the vSphere Client allowing read-only mode) and I'm restoring from the last backup before I made any changes.
Apologies for wasting your time.
Sorry for my confused answer... A mean:
connecting to vcenter, after a DNS problem, is possible by adding an entry in /etc/hosts file of your client. obviously this is not a definitive solution, but a method used in emergency.
Like said to vHaridas (and confirmed in the KB) is not possible to change hostname/ip.