I have no personal first-hand experience with merchant marine veterans' benefits but I have answered this kind of inquiry in the past so here goes.
Benefits for surviving spouses of World War II merchant mariners may be very limited, and may apply primarily for spouses of mariners who died in service, or died later of service-related injuries or health conditions. But there is no downside to pursuing a request for benefits, whatever the individual case.
Mariners, or their survivors, must first establish that they are qualified to receive benefits. That means being able to document that the mariner had oceangoing service between December 7, 1941, and December 31, 1946. This service must be certified by the U.S. Coast Guard, using records provided by the mariner (or survivors) and/or held by the Coast Guard. The mariner (or survivors) use DD Form 2168 to contact the Coast Guard; links to the form and other information are below. You will have to contact the Coast Guard's National Maritime Center in West Virginia; the exact address is available through the links below.
If the Coast Guard is able to certify qualifying service, the Coast Guard will issue a Certificate of Release or Discharge from Active Duty (DD Form 214). (This is the same discharge form that military personnel receive automatically upon separation from the military. Since merchant mariners were never a part of the military, merchant mariners did not receive this form upon completion of service.)
Assuming the Coast Guard issues a DD 214, the mariner (or survivors) apply for benefits through the Veterans Administration, using one or more of several Veterans Administration forms. See the second link below.
For more information see:
http://www.uscg.mil/nmc/wwiimm.asp (Coast Guard information)
http://www.vba.va.gov/bln/21/Milsvc/Docs/MerMar.doc (Veterans Administration information)
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website