Thanks, Simonta - yes, that makes sense.
The motherboard has two SATA sockets and I have two SATA drives plugged in there and working happily. The snag is with eSATA, for which I've got a PCI card. I would hope the MoBo BIOS wouldn't enter into that, and that the driver for the PCI card is what matters (or the BIOS on the card).
I've spent a happy couple of hours digging on various Win 7 sites. Not found an answer, but lots of other folks have the same problem.