I have been putting my DS on the charger for the last week or so and the little orange charge light comes on, only to go off a few minutes later.

I'm pretty sure the DS isn't fully charged and I think it used to get a Green light when it did.  I tried changing power points but it happens everytime, sometimes the light lasts only thirty seconds.

Is there a problem with my DS, or my charger?

When it's fully charged the light turns off - it's only green when the DS is on.

I guess the only way to diagnose this is to run an experiment - use your charger on someone else's DS, and use someone else's charger on your DS........problem solved! Well, not solved, but at least you'll know what's wrong.