The error message in question is coming from Windows, which is apparently having a problem accessing the private key for the certificate. Which version of Windows are you using? Do you have all updates from WindowsUpdate installed? Do you have any 3rd party encryption or SmartCard software (e.g. "Entrust") installed?
Your first step should be to disable HTTPS decryption and choose "Remove Interception Certificates." Delete all certificates and untrust from the certificate store.
Next, re-enable HTTPS decryption, allow the root to be recreated and retrusted. Then see if the problem goes away.
If not, try installing the Fiddler Certificate Generator plugin
and restart. Use the QuickExec box and type:
prefs set fiddler.certmaker.bc.Debug True
and hit enter. Restart Fiddler and do you see anything more in the Log tab when you try to navigate to a HTTPS site?