I have a HP 3100 Series 1.25X/2.5X/20X DVD+RW SCSI Drive. The drive is
not currently sold in the USA. I need an appropriate driver that would
allow me to use the DVD Writer to burn DVD's on Windows 2000 and Windows XP.
Please do not reply saying that there is no such driver, because I
know that such a driver does exist.

Full name appears to be HP DVD Writer 3100i

Here's the press release announcing it:

HP Announces Industry's First DVD+RW Drive
Palo Alto, California. May 24, 1999 
http://web.archive.org/web/19990913184014/http://www1.hp.com/pressrel/may99/24may99d.htm

So little info exists for it, (nothing remaining within HP sites) that
it could be possible that it was never actually sold to the public...

Have you tried DriverGuide.com? This is a massive resourse for all
hardware drivers. Cd-Rw drives, DVD-ROM drives; HDD even mice and
floppy drives.
This is an excellent site. Your sure to find the driver you need here!