both 1.3.1 and 1.4 should work
I am using j2sdk 1.4 and can not even start the service
C:\Jboss\jboss-3.0.3\bin>JBoss30.bat C:\j2sdk1.4.0 c:\jboss\jboss-3.0.3 server
'JavaService.exe' is not recognized as an internal or external command,
operable program or batch file.
That has nothing to do with the version of JDK you have installed.