Rose, I am a hobbyist and not an expert, but I believe the place for you to begin would be the National Personnel Records Center (NPRC). Click this link to go to their webpage regarding military personnel records: http://www.archives.gov/st-louis/military-personnel/index.htmlhttp://www.archives.gov/st-louis/military-personnel/index.html
(Among other info found there are particulars regarding the disastrous fire they had in 1973. However, you will note that Marine Corps personnel records were not affected.)
Your post "...service records for deceased veterans..." seems to indicate that the individual about whom you are seeking info died after he was in the Corps. Is this the case? In the event that the contrary is true, and he was killed in action, there are other sources you could pursue.