I have never owned either of your cameras so take this with a grain of salt. Both your lenses are D series and do NOT have a focus motor in them, they REQUIRE a focusing motor in the camera, which your D70 has, and your D5000 does not, that explains the lack of AF on that one.
From what you said I gather that both lenses function as intended on the D5000 (they both work without AF, the 300mm will AF, no other problems), this helps to tell us the lenses seem to be functional.
Next, the FEE error is to my knowledge always aperture. Try unlocking the ring, rotating it several times all the way through the range, then locking it back (while off the camera), then place it back on the camera.
If that fails, you can try cleaning the small metal contacts that pass information from the lens to the camera, especially the ones on the camera. Dirty contacts can present themselves on one lens and not another even though both work on a second camera because of minute differences in clearances and fits on the different bodies.
If that fails, you need to send your lens and/or body in to Nikon and have it repaired.
Allan