Finding exact statement causing error 3930
In Profiler, click "show all events" and go to the Errors and Warnings listing.  You should be able to check Exception and User Error Message.  The Exception class will show you the actual error and User Error Message will show you the message displayed (e.g., "Incorrect syntax near ..." or whatnot).

You mention a message going into the error log; there's also an ErrorLog event in the Error Message category, so it wouldn't hurt to include that as well.

You would need to include the SQL:BatchStarting and possibly SQL:BatchCompleted as well to get the command being run at that time.

You might also look at Remus Rusanu's answer to an earlier question of this nature to see if that might help solve the problem.