Slow connection to SQL Server both locally and by client
There is no way to see performance in the past unless you have a monitoring system in place during the event in question.

Assuming you don't have a monitoring solution in place, you could be prepared in case this happens in future.  

For instance, you could look at wait stats over a time period using my wait stats capture script.  The script shows what SQL Server actually waited on over a short period of time.  For instance, if you happened to run that script while the problem in your questions was occurring, it's possible the output might show thread starvation via the THREADPOOL wait.  Check Paul Randal's site for details about that wait.