How much do starlight and artificial light illuminate the Moon? The Moon receives most of its light from the Sun, either directly through sunlight or indirectly through Earthshine. However, there are many other dimmer sources of illumination. 


Starlight. This is probably the most important one. Under exceptional conditions, it creates shadows here on Earth.
Artificial light. Mostly city lights and gas flares.
Meteorological activity. Lightning storms on Earth and other planets are visible from space, and here on Earth, they can trigger other sources of light such as firestorms.
Bioluminescence. Light-emitting microorganisms are bright enough and numerous enough to be seen from space.
Transient bright lights. Events such as supernovas and asteroid impacts are rare, but when they happen, they are a significant source of illumination. Over long timescales, for example a billion years, this may be the biggest contributor of non-solar light.


How much do these light sources illuminate the Moon? If there was no Sun, could we still see the Moon with these lights? And of the three Earth-based sources (artificial light, meteorological activity, bioluminescence), which one illuminates the best?
To reverse the question: if you were on the Moon, what sources of light would you see?


The Sun would be the major source of light.
Although the Moon's albedo is only about 12%, reflected light from the ground would be the second major source.
The Earth would be in a poor 3rd place. You could see the general shape of the continents, but not storms or any other light-emitting meteorological or biological activity (it's there, but much too faint to be seen from the Moon)
The other planets would be poor 4th place.
Starlight would be in a poor 5th place.


It would be similar to standing on Earth, except:


The Moon has no atmosphere, so:


the Sun would be brighter
there'd be no light diffusion, so you could see the Earth/planets/stars in the daytime
Meteors would not leave a fiery trail -- they would simply hit the moon silently. Asteroid impacts on the Moon would also produce no sound.

There wouldn't be a moon in the sky, but there would be an Earth instead.


You add a twist to the question by asking about past and future light:


In about 7.6 billion years, the Sun will expand to (probably) engulf the Earth and Moon, which will probably be the most light the Moon will see before it's reduced to nothingness.
The Moon possibly saw a lot of light when it was created through planetary collision. Not sure this counts, because the Moon didn't really exist until sometime after this.
Any other major source of light (such as supernovas) would be visible from Earth as well. That doesn't mean there haven't been any super-bright supernovas, but if they were bright enough and lasted long enough to generate more light than the Sun has during its lifetime, they would probably have a major impact on Earth (who knows, maybe that's why the dinosaurs died ), and there's really no evidence anything that liked happened.