Based on the limited facts provided I assume that Gary was born some time in the 50's or or early 60's, based on when you were born.You also know what I assume are brothers, and possibly his mother.It appears you have a few dates also.
The first thing you should do is record all of the information you have in a form that you can see the various relationships.Biological you need a man and a woman to produce a baby.So the chart you create should use that as a starting point.As you find the people to fill the blanks you can added notes as to the status of the marriage, as it may help in your search.If you don't know the exact date, I would also approximate the ages for each person know or unknown.Knowing these dates will help in searching.You have meet your father so you may be able to place his birth date to a decade. But if you don't remember then he was probably no younger the 18 at your birth and probably no older that 50.You can use the same rule for approximating other people's birthdates.
With this recent of birth you may have trouble finding things online with the privacy laws.But this does not mean it is impossible to find something.
The best starting point for your search is Familysearch (https://www.familysearch.org/)There are several Gary Snyders listed as Snyder, Snider, and Schneider.
One other source that can be checked is Find a Grave, that is very good for recent deaths.
Another source are the newspapers in the last known area where Gary is known to live.You may find hisMarriages, an arrest, separation notice, or the like. Google Newspapers is a nice place to start. Be aware you may have to go through page by page as they are indexed using OCR.
There is a very good list of obituaries at http://www.legacy.com/NS/http://www.legacy.com/NS/ This is a good site not only for obituaries but it also list people who have been found from other listing. (I recently found a lady who I thought was dead.She is living in my home town at 98 years old.)
Finally if you have checked the above and and found nothing you may check the search engines like Google, Ask, Yahoo, etc.When everything else has failed you can sometimes turn up leads.