Some people addressed the question of "possible life forms that would evolve" rather than point out that life on Earth as we know it would not work. I will keep going in that direction.
There's nothing about our specific nature that makes us more alive than a completely neutral object like a rock. Even though plants are made up of complex cels like animals are, a plant is more like a highly dynamic static object such as a rock, while animals containing a nervous system are able to store information and act, anywhere in the range of a jellyfish (non centralized nervous system but still maintaining an energy state) to a human (highly centralized and more information stored and manipulated).
So, for the question of life, let's start with finding if an energy state can be maintained rather than the typical reproduction centered meaning of life.
I think most of what we consider life is an insulating membrane, and the ability to take input and produce output in a controlled, predictably beneficial way. Mitochondria (energy production organelle) do this, and they are theorized to be the first kind of living organism. They also have their own DNA.
One could theorize that the very first existence of life was slice of DNA-like reproductive material, which in some medium was able to influence the creation of some type of protein-like molecule that enabled more reproduction of the material and thus more production of the protein. Basically it was taking energy from the environment and threading it along some delicate pathway. It is unique form of chemical reaction, in that it leaves a memory of itself in different forms as the DNA-like material. Thus, as it multiplies and tweaks the reaction, it is able to try many forms with the hope of identifying a new path-of-least-resistance, while not abandoning previously successful forms.
Eventually, the reproductive material that produces the protein and reproduces itself starts reproducing itself with a sequence that codes for a protein that influences the development of a membrane, which has a positive effect on the reproduction/proteins system. This is the basic theme established- a system based on stored information that drives a specialized metabolism will establish ways to ensure a controlled development. It's a positive feedback loop that implements its own homeostatic environment. This theme should carry us from a Mitochondrion, to a cell, to a multicellular organism, to a human with a brain.
I could see "gaseous cloud" beings as someone mentioned, possibly having some type of light membrane material inside of and around itself.
I could also envision something evolving in liquid rock and possibly engineering a way to leave access the surface. There could be a type of chemical stew that produces a really good insulating material, and this could exist in a vacuum. Like rubbery chemical beings. One could wonder if metal could become sentient if it was able to manipulate a charge.