If he was wounded, he may have applied for benefits through the Dept of Veterans Affairs. If he did, they should have a file on him with info that would include his Marine Corps serial number. The phone number to make your initial inquiry with the Dept of VA is 800-827-1000.
You should also be able to get his service record from NARA. (The big 1977 fire did not affect Navy Dept records.) This will no doubt be easier with his serial number, so you might want try to get that first through the VA. Info on how to proceed in obtaining his service record can be found at this address: