My dad served during 08-11-1955 thru 08-10-1960 he had an honorable discharge but they said he didn't serve during a time of war so he cant get benefits . I am still currently searching to find something I heard that they do have programs for all veterans but I have yet to find anything
http://benefits.va.gov/benefits/ is your best starting point since you have not mentioned if any service disability occurred, status of discharge etc. There are also articles on veterans benefits on this website that can be accessed by using the "search" function.