it says /tmp does not have free space. Have you tried rebooting the appliance ? Please try rebooting the appliance once, during reboot /tmp will be cleared off. Service may come up again.
Yes, you can deploy a new VCSA but you will lose all your VC data . it will be like your brand new vCenter and you have to add the hosts to new vCenter server.
Reboot has not solve the problem, I will try to increase size of disks and if It fails, reinstall the VCSA.