A man registered for the draft and those records are not available online. The WWII cards online now are the "Old Mens" one (b. 1871 to 1900) and the men filing then are all passed away, so no privacy or id theft problem.
WWII Military men did not use a Social Security Number on Service records or ID's. They were issued a military "Service Number". It was not until the 1970's did the Military switch to using SSNs and dropped the serial one. Unless he lived after at 1973 and received Veterans Benefits would he have had his SSN added to records.
The Marines will not have information on his dependents unless he listed them for housing needs or transportation needs provided by the government while he was in the service. Before you can get copies of his service records you have to be next of kin and have the proof.
Contact the NARA (they have service records and Marines were not burned in 1973 fire)and ask what can be done for you, if anything, to help. www.archives.gov