A hidden layer can still be the active layer. Make sure to select another layer from the panel before pasting.
I believe I am.
The new layer is selected. But no matter what I do it keeps trying to paste to the old layer (the layer from which the copied material derived).
In fact, I've even selected items in the new layer and hit paste inside... but again, no luck.
There's an option in the Layers pallet menu Paste Remembers Layers. Uncheck that, and it will work fine.
Yep, that's it.
I had used it for another project a few days back.
Thanks very much to you and everyone else who responded.