Best Auto focus Tele For Nikon D40

Yes.

If your lens is 8 months old, it is still in warranty. Contact Nikon for return instructions.

Seems as if you're snapping the shutter before the lens has focused. Have you tried manual focus or single-server auto focus?

Please check your focus settings in the camera menu. Play around with the focus point from Single to 11 points. Also, try Auto mode as a quick way to test if the focus is working

It sounds like you had the lens set for manual focus when you took the A / M switch plate off. If this was the case then when you but it back together the little arm behind the plate is on the wrong side of a moving gear assembly.

To fix, remove the auto/manual focus switch plate from the camera (just the one screw not the ribbon beneath) Push the switch over to A. Hook the bottom of the plate back to the lens and put the screw back in. Done!

Nikon: Nikkor 55-200mm f/4-5.6G IF-ED AF-S VR Sigma:70-200mm DG HSM

Which camera are you using? If the body has AF/MF switch, put that also to MF.If this fails to help, take out the lens and try to change it to MF.

with your D40, you can old go on manual focus on the 70-300mm AF-G/D nikkor.

This lens, afaik, does not have auto zoom - it has auto focus.

First the auto focus motor is in the body and not the lens so that will not be the problem. Unless you dropped the lens the problem is probably in the focus gear interface inside the lens ( it is stuck in the manual drive --that is why no autofocus-- and there is something preventing normal gear operation). Seems like a small problem but will require a look at the rear of the lens where the gear box is situated.