OK, here's what I did:
Tried a new user account on the basis that I may have a borked profile. No different.
Uninstalled/reinstalled fax service - no different.
Reseated fax modem, reseated ram - no different.
Updated motherboard drivers, checked for BIOS changes - no different.
Swapped fax modem card for another I have in a different box - Bingo!
So it was the card and all through that, W7 was looking me in the eye & saying, no guv, everything's alright here! Looking back, I suspect the thunderstorm may be repsonsible - it was right on top of the building & the lightning strike set off alarms in the car park.