If you can't connect remotly, or via DAC then try locally on the server itself. If you still can't connect the only thing I can think of is to restart the SQL instance.
Check your recompiles - use perfmon, under SQL Server: Statistics take a look at Batch Requests, Compilations and Recompilations. Compiling takes CPU, which unavoidable. Recompilations are a problem - if you are using embedded SQL try switching to stored procedures.
Analyse master.dbo.syscacheobjects to see if objects are being dropped from the procedure cache due to memory contention.
Also run profiler, and trace recompilations to see what code is causing recompilations (if you think that is causing your CPU).
Another possibility for high CPU is corrupted software and drivers. I know the guys here had an old version of a Java ODBC (JDBC?) driver that caused CPU to spike. A upgrade fixed the problem. Check google.
When in doubt - test, test, test!