I'm using my HP SJ5P scsi connected scanner with VISTA, as I did with
W2K and XP, by installing HP's old-time Deskscan 2.9 software that
includes TWAIN for communication.
Works perfectly. Download it from HP; install it using Compatibility
Mode set to XP with SP2 and check Run as Administrator (ask if you need
help on this) and it promptly found the scanner. It includes a very
nice Copier Utility that combines the scanner and your printers into a
first class document copying utility.
You can download the Deskscan 2.9 software from this HP SJ5P XP
I can't guarantee that it will work with the SJ3400c but it is worth
trying IMO. Back in the days when I was on the Team HP on Compuserve we
often recommended the Deskscan 2.9 instead of the Precisionscan
software that was being delivered with scanners then. I see your
SJ3400C uses Precisionscan.
Good luck and let us know how you get on.