<<<Yes, the COOLPIX S4300 is compatible with the SDHC cards. A new memory card needs to be formatted using the camera; it cannot go thru different cameras because that will damage your memory card. Try formatting the memory card with the card reader and then with the camera. Also, verify that is not write protected.>>>
I've never heard of cards being damaged by re-use in various cameras -- requires reformatting of course, but not damaging to the cards.
At any rate, we have since tried a third SDHC card (SanDisk 4GB class 4) that also brings up the same error ("this card cannot be used").
All cards have been reformatted to FAT32 using the card reader and computer. The camera will not allow formatting of the cards -- it won't proceed to the menu beyond the "card cannot be used" error screen.
None of the cards are write-protected.