Errors:

An error occurred during an attempt to perform the configuration task: An error occurred during an attempt to access the private key of the certificate with thumbprint XXXXXXXXXXXXXXXXXXXXXXXXXXXX'.  Confirm that the certificate has a private key and that you have permission to read the private key, and try again.

or

An error occurred during an attempt to perform the configuration task: A certificate with the thumbprint XXXXXXXXXXXXXXXXXXXXXXXXXXXX was not found in the My certificate store.

 

Solution:

This one was killing me for darn near a whole day.  No matches online for the errors, so hopefully these find someone else.  The problem occurred when I tried to join a second federation server to my ADFS farm.  Basically, the thumbprint found in the XXXXXXXXXXXXXXXXXXXXXXXXXXXX refers to the one on your *primary* server; not the one you're adding.  So, you have to replace the certificate you bound to the default website with the one from the primary federation server.  You do this through MMC > Certificates > Local Computer > Personal Store > Export.  Copy that over to the server you're trying to add to the farm and import it to the same location using the MMC again.  Finally got past this thing.  Phew!