SQL Server service unresponsive
Need more info like SELECT @@VERSION, do you use CLR procs, have you set max memory on both the instances? Were you able to look at which spids were taking most resources and why? 

To catch the intermittent cpu spikes, you may have to setup a trace and here is one such script.

http://www.sqlsoldier.com/wp/sqlserver/catchingtransientcpuspikesusingsqltrace