As a follow up, when I do use the Client Certificate Management and change the IP to my current IP but leave the computer name the same, it sees my computer but cannot get WMI connectivity. Just as extra information.
Got the answer from tech support. I'll post it here so it'll help others.
The certificates have to go into the Trusted Root Certificate Authorities and Trusted Publishers stores under the computer account. This means you have to open mmc and add the certificates snapin. Select Computer Account and then the machine (for me it was local). Then the cert should be used properly.