Thanks, guys, for the excellent ideas. I brought it in to Henry's. They tried a new battery and presto - it worked! It turns out that BOTH of my batteries are near the end of their life. I had two from my old - and still going strong - C7070WZ and they must have been the ones (at least I'm hoping I don't have any more problems). The lens that I first noticed it with was the 70-300mm, but then I switched lenses and it didn't seem to make a difference.
Anyway, thanks again,