Have you turned on your VR? Have you taken the same photo using auto focus? Try taking a photo with your camera on a table say, and use the delayed shutter release (hands off camera) to see if your image is sharp. You could also try this website below if all else fails to narrow down the problem to a) Is it me? 2) Is it the camera?
You are going to have a hard time holding steady at 300 mm DX (450 mm equivalent on FX) and that shutter speed. General rule of thumb is to keep your exposure speed at the reciprocal of the focal length. You can push it a little slower with VR on but not too far.
In this case if you had bumped the ISO to 800 your shutter speed would have been fast enough to prevent motion shake. Your D3100 will give good results at ISO 800, don't be afraid to use it if needed.
working on it in Middle TN Nikon D3100
35 mm 1.8 Nikkor 18-55 mm Nikkor VR 55-200 mm Nikkor VR 55-300 mm Nikkor VR 150-500 mm Sigma OS MeFoto Road Trip w/Q1 ballhead Feisol CT3471 & Markins M20 ballhead