Shooting video at night without enough light is almost impossible. You can pump up the ISO which will result in a grainy image or use an extra light source. In case you are searching for a portable but still powerful light source for run-n-gun shoots you should take a look at the dimmable Z96 LED video light. Build quality is good, the light is very bright and also dimmable, you get 2 diffusors and a shoe mount to put it on top of your camera and it works with 5 AA batteries. If you need a bigger light source you can get more of these and stick them together. The LEDs on mine Z96 don't have the same color. Some are white, some purple and some yellow. But this doesn't affect the light at all.
Check this post on cheesycam.com for more information.
I was really happy when I got mine. Tested it with an AC adapter (not included) and it worked really good - I'm still using it as my desk lamp with the AC plug. But when I put some batteries in it I noticed that it started to flicker after a while. First I thought it was a problem with the LED light but then I realized it was because of my batteries.
So if you need a strobe (maybe for a music video or to simulate some flashes) - this is how you get the effect: simply take 4 fully loaded AA batteries instead of 5 and stick in another empty battery. Then twist the dial till you reach the brightest light (not at the end any more but somewhere in the middle) and adjust it slightly till the light starts to flicker. Once it started to flicker you can adjust the strobe speed by twisting the dial. For me this effect is reproducible, I don't know if it works for every Z96 LED light.
Hope this was interesting.