The D40 (and the D60) do not have an auto-focus motor in the camera body. Hence, they will not auto-focus with older lens which do not have an auto-focus motor in the lens: you need an AF-S style lens. Nikon (and third party vendors of Nikon mount lens) are moving towards up-dating lens with AF-S. The AF-S offers advantages over the body motor approach in terms of speed, quietness, etc.
The design route taken by Nikon and Canon is interesting (
see here). AF lens first appeared in 1987/8. Nikon opted for backwards compatibility with its older lens by retaining their lens mount system and putting the lens motor in the body. Canon on the other hand, changed their mounting system and put the motor in the lens from when they first produced AF lens (1987). This caused major problems for Canon cameras at the time since there was no backwards compatibility with older lens. Nikon's first AF-S lens was made in 2000 .
It's always delicate if a spouse buys a gift which isn't ideal

However, in addition to the auto-focus issue, the 70-300mm G lens does not get great reviews for its optical properties and performance (see
here and
here). The AF-S version at this focal length (the
Nikon 70-300 VR) has much better reviews, will AF on the D40 but does cost more

The 55-200mm VR doesn't get quite the same reach but also AF's on the D40 and gets generally good comments.