Yes, definitely use a blower to start with. My comments were based on experience cleaning earlier CCD cameras, which tended to have more serious dust problems because their use of electrical charge would often cause dust to adhere due to residual charge even after the camera was turned off. Current CMOS cameras shouldn't have this issue and will respond better to air, but be careful to make sure you don't use air from a source that contains condensation, oil, or other contaminants. Anything purpose-built for cleaning cameras is probably OK.
Edit: If you feel that those conditions were an uncommon thing, sure, send it back to Nikon. They'll clean the camera thoroughly and safely. Not sure if or how much they charge for that. However, if you're struggling with dust due to the circumstances under which you shoot your preferred subject, you'll have the problem over and over again.
One tip which has helped quite a bit for me is to make sure to always tilt the camera slightly toward the ground when changing lenses. If you point the camera straight up to do this, you're a lot more likely to have ambient debris settle into the camera, but orienting the mount opening toward the ground lets gravity work to pull dust away from the sensor rather than toward it. Doing this is not a complete solution but it does help in any but the most extremely dusty environments.