Hello Luke,
Explore every angle while trying to work out whom/where root passwords may reside - even just one ESXi root with the necessary datastores attached should be sufficient. If not then start working out what you need to be able to re-install a host (or install/use a spare one you have on hand) and connect it to the necessary storage e.g. are these iSCSI or FC which will require zoning or NFS which will require permissions. You mentioned "- all IP addresses and credentials are stored on the network which I naturally can't access" - Do you mean that everything is stored somewhere you cannot access over the network (and thus inaccessible with no network)? Or is this stored on a site that you can physically access?
Bob