Hello Don,
"For whatever reason, upon power up the newly registered VCenter server has lost all configurations, to include IP address"
vCSA or Windows-based? Lost *all* configurations or just no network connectivity?
Are you using vDS here? There can be issues with vCenter not having it's previously assigned port available - there are workarounds to this such as 'borrowing' a NIC on a host to make a vSS and using this (or if you want to get esoteric about it: stealing the port of another VM is technically feasible).
"(3 hosts, 1 witness)"
As in a 2-node + 1 witness or some form of lop-sided stretched cluster?
Is all the vSAN data currently healthy/accessible?
Run on any clustered node:
# cmmds-tool find -f python | grep CONFIG_STATUS -B 4 -A 6 | grep 'uuid\|content' | grep -o 'state\\\":\ [0-9]*' | sort | uniq -c
"Unfortunately, the one host in question is the only one that cannot access the VSAN and to make matters worse, it was the host where VCenter VM is located."
Do you mean to say one node cannot join the cluster? Test the vSAN netowrk connection inter-node:
# vmkping -I vmk<vSANenabled> <IPofOtherNodesvSANvmk>
If this functions then you need to start looking at the ports that are used for inter-node communication which depends on what build you are using (5.5-6.5 use Multicast - 12345, 23451 (UDP), 6.6-6.7 uses Unicast mode on port 12321 (UDP)) and/or the unicastagent lists if on 6.6/6.7 - you did apparently rework the IPs of the hosts so if on 6.6/6.7 do check the lists as they won't have changes pushed down by vCenter if it is down.
https://blogs.vmware.com/vsphere/2014/09/virtual-san-networking-guidelines-multicast.html
https://kb.vmware.com/s/article/2150303
"What can I do to solve this issue? I have exhausted my troubleshooting steps and would incredibly appreciate any guidance. Thank you very much."
If you have a support contract and/or this is a production workload I would advise opening a Support Request with us at VMware GSS.
Bob