I too have a HP ScanJet 3300C, and just got a new computer with Vista.
A search for drivers on the HP site gives this:
"We are sorry to inform you that there will be no Windows Vista support available for your HP product. Therefore your product will not work with Windows Vista."
I don't know who to swear at, Microsoft or HP.
I guess it's not HP's fault that Microsoft changed Windows so much that the drivers have to be rewritten for Vista. But then, HP never bothered to update the driver for this scanner for Windows XP either.