I also encountered the same issue and make sure that all the prerequisites are installed on my 2008 server properly. I have retried with different method found on internet and none of it is work in my case.
Then i starting to do some troubleshoot and eventually found that when deploy Azure Connected Machine agent version higher or equal than 1.40 will have the same error. So, to deploy the 2008 server to azure arc, you can either download version 1.39 from
Official release notes
Direct download link from release notes
Then connect the 2008 server to your azure resources through azcmagent cli
https://learn.microsoft.com/en-us/azure/azure-arc/servers/azcmagent-connect
OR
Rewrite the ps1 script to download version 1.39 instead of latest version Azure Connected Machine agent
Have already opened a support ticket on this issue and reported to Microsoft, and from their reply seems that version 1.39 is the last planned version to support 2008 server.