You will probably need to look at several resources in order to solve this puzzle.First, you should probably look at birth, death, Social Security, and/or marriage records for your father and grandparents in the county or counties and newspapers that they lived in. You may also want to check property and tax records.Also, the 1940 census should be coming out in another year.It may take some time for it to be indexed, but you could either join Ancestry or find a genealogy library that has access to Ancestry.
For more information about how to proceed, Cyndi's List is an invaluable website.If you get stumped, you can also go intoGenForum chat room #1; there are frequently experienced researchers there that could help you resolve a small, concrete question.(They probably won't be familiar with Hinmans.
Last, but not least, I hope you have already looked at the Hinman family webpage!Browse the other older posts on this page, especially those mentioning the late Munson Hinman, who worked very hard to compile it from the research of many other Hinmans.It may not have your father or grandparents, but there is a good chance that it would have a great-grandparent.Once you discover a great-grandparent, come back to this page and post a query with that name, with also a county or DOB if possible, in the Subject line.The more specific you are in your subject line, the more likely you are to find help.
Also, Ancestry has another message board that gets quite a bit of traffic.If you haven't posted there, it would probably be a good idea.