Action shots in artificial light.

[IndyAnna]

My photo interests range from outdoor wildlife to indoor sports. I currently use a Nikon 8700. I have tried for years to take pictures of nieces and nephews playing various sports from football and soccer to basketball and volleyball. When it comes to getting the shots in any type of artificial light--indoors or night games-- they either end up bright and blurred or dark green. I was wondering if I just have not mastered the settings available on my current camera or if I need to consider different equipment. I have tried many combinations to no avail. Most of the gyms discourage the use of a flash. Thank you for any input anyone might have.
I am very new to navigating this forum and think I just posted this in another section a few minutes ago.

[autofocus]

Really hard to do well with a point and shoot...but you already know that. This type of photography calls for a DSLR with a fast zoom lens such as a 70 - 200mm, F/2.8. (a $2000 - $3000 investment is probably what you could be looking at for a combo like this) Even with that, it can be tricky exposures to get right.