SQL Server freezes (because of application), need logging
SQL Server has a Dedicated Administrative Connection, see How to: Use the Dedicated Administrator Connection with SQL Server Management Studio. The DAC uses distinct, pre-reserved resources (memory, CPU, IO ports etc) exactly so it can be used even when the server is 'frozen'. From the DAC you can run queries that can identify the cause of the spike.

When the server is restarted the ERRORLOG is not deleted, it gets recycled. The errorlog from before the shutdown is usually ERRORLOG.1, then ERRORLOG.2 etc, and is located in the same folder as the current one. Just open it and inspect the tail of the file. Your previous restart logs are probably there still, have a look and see what you can find. Also see if there are any .mdmp files in the same location...