Here is what I would try.

You say the local Administrator account password is the same for ALL workstations in this workgroup - YES?

1. Make sure all workstations are in the same WORKGROUP name.

2. Logon to your workstation with that same Administrator/Password.

Then try running Regedit or other Admin tools and it should operate those tools as though you were logged on to that system as they Administrator.

The account name and passworkd MUST match on both systems.

If that all works then try the WMI. If it does not work then you need to modify the "root\cimv2" connection permissions and also verify that the "root\cimv2" is still the default connection namespace and that someone has not renamed it.