I am thinking that all sports would pretty much be impossible based on your description of yourself except for the following:
I think for shooting and archery it would take about 15 minutes to determine if you had any world class potential in those sports, and it would definitely be a longshot.
Sailing and Equestrian, I don't really know much about. Obviously either would require significant investment (buying a boat or a horse and a bunch of things to jump over).
So.....I would say without significant investment you are at least 1000-1 against competing for the U.S. You are also at least 100,000-1 against winning a gold medal.
Your chances would improve for the competing part if you were competing for a smaller or less developed country. Also, your chances would improve if you say...doped yourself with your own blood, then you might stand to do well in cycling