Finding Royal Marines records

Stop Press The National Archives | DocumentsOnline 2009 has Royal Marine service records

In 1855 the whole marine corps took the name Royal Marine Light Infantry
(Red Marines). In 1859 a separate Division of Royal Marine Artillery (Blue
Marines) was formed, but in 1923 the two merged to become the single corps
of Royal Marines.

http://www.lightinfantry.org.uk/regiments/rmli/marine_index.htm

http://www.royalmarinesregimental.co.uk/

http://www.royalmarinesmuseum.co.uk/

service records http://www.veteransagency.mod.uk/service_recs/service%20_recs_rn.htm

also TNA/PRO at http://www.catalogue.nationalarchives.gov.uk/default.asp

has the following ADM files  (ADM means Admiralty)
  Records of Individuals
  Attestations 1790-1883 ADM157/1-139
  Description Books 1755-1884 ADM158/1-32
  General Weekly Returns 1755-1869 ADM183/42-98
  Discharge Books 1773-1884 ADM183/101-110
If you cannot get to their offices at Kew then professional researchers can
be employed - PRO did have suggestions on their pages

Royal Marines Historical Record Office
Centurion Building  HMS Sultan  Military Road Gosport PO13 9XA
Should be next of kin