800 dude is spot on - talent will tend to matter less as the competition pool decreases.
So, you'll want to look for sports with two properties: i) barriers to entry, and ii) low rewards (especially monetary). A third property would be region-specific sports (like jai jalai), but I don't think that's what the OP has in mind.
Barriers to entry would be things like cost of equipment and natural factors out of our control. For example, ski jump requires snow and a mountain, or as an alternative a very expensive facility (I've never heard of an indoor olympic-style ski jump, but I'm sure it's possible). You also need some gear. Bobsled is similar but even more expensive gear.
For low rewards, think of a sport like ultramarathoning. Prize money is small and there is little opportunity for sponsorship compared to even olympic track & field athletes.
I think that winter sports might be a good bet. For 'activities' (though these guys are under a lot of physical stress) I would imagine that motorsports (despite having large prize money) could be a good possibility, simply because the barrier to entry is so high.