Question: Are there other life giving sources of energy in space apart from stars? (like nebulae, radiation, etc.)? Or are all possible life giving potential sources some variation of a star?

Answer: 
There are three important sources of energy in planetary bodies (or their moons) that may be important in determining their suitability for life. All of these are evident in various bodies in the Solar System.

The first is tidal heating. When one object orbits another then there will be gradient in the gravitational force across their finite sizes. If this is combined with any orbital non-circularity or difference between rotational and orbital periods, along with some fluidity in the structure of one of the bodies, then it will be heated by frictional forces as the fluid moves in response to the changing gravitational gradient. This heating is most evident on Io in our own Solar System, the closest large moon of Jupiter, and is generally more important for objects orbiting close to more massive stars or planets.

The second is heating by radioactive decay. When planetary systems are born, they can incorporate significant amounts of radioactive material. Some of this has a short half-life and may be responsible for a short period of intense heating, but other isotopes are much longer lived. According to [this article](https://blogs.scientificamerican.com/observations/nuclear-fission-confirmed-as-source-of-more-than-half-of-earths-heat/), about 20 TW of power is generated inside the Earth from the radioactive decay of uranium, thorium and potassium. This sounds a lot, but is about a factor $10^4$ less power than we receive from the Sun.

The third source is just the "heat of formation". Gathering together the raw materials of a planet/moon and compressing it into a gravitational potential well, inevitably leads to the generation of considerable heat and it can take billions of years for this heat to leak out into space. Indeed, for the Earth, the heat of formation is probably comparable with radioactive decay in terms of supplying energy to the surface from the interior.
ProfRob makes a good point about tidal heating, but you can have internal heat sufficient for life even without this. The heat I'm referring to is heat trapped in a planet's core from its formation, which slowly and reliably leaks out through geothermal vents.

We observe this at the bottoms of Earth's oceans, where thriving colonies of deep sea organisms live in total darkness, feeding off the heat and chemicals that come from these vents. No sunlight supports these organisms, only geothermal energy.

Note that how long this is useful depends on your planet's size. Mars used to have a liquid core, but has since cooled down enough to have its core freeze since it's smaller and therefore cools faster. The larger your planet, the longer it'd be able to provide this trickle of heat.

---

Edit: it has been made aware to me that Earth's internal heat is mostly driven by radioactive decay nowadays, which I didn't know. The point still stands however that a planet's original heat could be sufficient to jumpstart life. I'm not sure how long it could provide for this before something else would need to kick in though.