Return sql rows where field contains ONLY non-alphanumeric characters

SQL Server doesn't have regular expressions. It uses the LIKE pattern matching syntax which isn't the same.

As it happens, you are close. Just need leading+trailing wildcards and move the NOT

 WHERE whatever NOT LIKE '%[a-z0-9]%'

If you have short strings you should be able to create a few LIKE patterns ('[^a-zA-Z0-9]', '[^a-zA-Z0-9][^a-zA-Z0-9]', ...) to match strings of different length. Otherwise you should use CLR user defined function and a proper regular expression - Regular Expressions Make Pattern Matching And Data Extraction Easier.