I have a possible source to find the service number of a person who died in WWII. You need to know the person's state and county. If you only know the state, then you have to spend the time to go through each county.
World War II Honor List of Dead and Missing Army and Army Air Forces Personnel:
This document lists by state War Department casualties (Army and Army Air Force personnel) from World War II. Entries in the state list are arranged by name of county and there under alphabetically by name of deceased. Information provided includes serial number, rank and type of casualty. The birthplace or residence of the deceased is not indicated.
See Related Resource: World War II Casualties for Navy, Marine Corps, and Coast Guard