Hi Explorer,
This is an interesting question, but genetic science suggests that all life shares one common origin. I think that AZPaul3's point about the post-life world being hostile to new life is a good one. Living organisms have an enormous effect on Earth's atmosphere, and have done ever since blue-green algae ruled the world, which they did for billions of years. Over this time they increased the oxygen content of the atmosphere. It might be that the process that originally started life is not possible under modern conditions.
On the other hand, maybe we'll eventually find a hydrothermal vent or cave system with life forms unrelated to our own. Who knows?
Mutate and Survive