Sony VAIO F-series laptop with a built-in Conexant SoftK56 Data,Fax PCI Modem
PCI VendorID=14F1 DeviceID=2443

Here's how I got it working with KNOPPIX V3.2 2003-05-16 EN:

1. Boot into a text console (no X!)
knoppix 2

2. Ensure date and time are correct for local time zone
cp -p /usr/share/zoneinfo/US/Pacific /etc/localtime
hwclock -s

3. Get a copy of the Linuxant HSF source distribution onto the machine somehow

4. Unpack tarball
cd /ramdisk
tar xvpzf /PATH/TO/hsflinmodem-5.03.27lnxtbeta03042700.tar.gz

5. Start at the top
cd hs*

6. Edit config.mak
(old line 23) HOME=
(new line 23) HOME=/ramdisk
(old line 31) HSFETCDIR=$(ETCDIR)/hsf
(new line 31) HSFETCDIR=/etc/hsf
(old line 32) HSFINFDIR=$(HSFETCDIR)/inf
(new line 32) HSFINFDIR=$(ETCDIR)/hsf/inf

7. Edit modules/common.mak
(old line 22) KMODS_DIR= /lib/modules/$(KERNELVER)
(new line 22) KMODS_DIR= /ramdisk/lib/modules/$(KERNELVER)

8. Edit scripts/hsfconfig.in
(old line 1118) depmod -e -a
(new line 1118) depmod -e -a -b /ramdisk
(old line 1495) PATH=/usr/sbin:/sbin:/usr/bin:/bin:/usr/local/sbin:/usr/local/bin
(new line 1495) PATH=/usr/sbin:/sbin:/usr/bin:/bin:/usr/local/sbin:/usr/local/bin:/ramdisk/usr/sbin

9. Compile stuff [don't think, just follow directions]
make install
/ramdisk/usr/sbin/hsfconfig -a

You'll get a warning:
depmod: Can't open /lib/modules/2.4.20-xfs/modules.dep for writing

Ignore it!

10. Gather the few pieces actually needed for this particular model
cd /ramdisk
mkdir -p hsf/etc.hsf hsf/modules/misc
cp -p /etc/hsf/nvram.bin hsf/etc.hsf
cd lib/modules/2.4.20-xfs/misc
mv hsfbasic2.o hsfengine.o hsfosspec.o hsfserial.o /ramdisk/hsf/modules/misc
cd /ramdisk
tar cvzf hsf.tgz hsf

11. Make customization script (see /etc/init.d/alsa-autoconfig)
cp /etc/modutils/hsf knoppix.sh
chmod 755 knoppix.sh

Add "glue" so it looks like:

#!/bin/sh
(cd /ramdisk;exec /bin/tar xpzf $1/hsf.tgz)
/bin/ln -s /ramdisk/hsf/etc.hsf /etc/hsf
HSFPATH=/ramdisk/hsf/modules
export HSFPATH
/bin/cat << EOF > /etc/modutils/hsf
path[misc]=$HSFPATH
depfile=$HSFPATH/modules.dep
generic_stringfile=$HSFPATH/modules.generic_string
pcimapfile=$HSFPATH/modules.pcimap
isapnpmapfile=$HSFPATH/modules.isapnpmap
usbmapfile=$HSFPATH/modules.usbmap
parportmapfile=$HSFPATH/modules.parportmap
ieee1394mapfile=$HSFPATH/modules.ieee1394map
pnpbiosmapfile=$HSFPATH/modules.pnpbiosmap
alias /dev/ttySHSF* hsfserial
alias char-major-241 hsfserial
alias /dev/ttyCUA* hsfserial
alias char-major-242 hsfserial
alias /dev/modem hsfserial
options hsfserial serialmajor=241 calloutmajor=242
EOF
unset HSFPATH
/bin/rm -f /etc/modules.conf
/sbin/update-modules
/bin/rm -f /dev/modem /dev/cuaHSF0 /dev/ttySHSF0
/bin/mknod -m 666 /dev/ttySHSF0 c 241 64
/bin/mknod -m 666 /dev/cuaHSF0 c 242 64
/bin/ln -s /dev/ttySHSF0 /dev/modem

12. Put the files on a [blank] floppy
fdformat /dev/fd0H1440
mkfs /dev/fd0H1440
cp -p hsf.tgz knoppix.sh /mnt/floppy
sync

13. Try it out
shutdown -r now

You'll get a warning:
insmod: Note: /etc/modules.conf is more recent than /lib/modules/2.4.20-xfs/modules.dep

Ignore it!

Boot:

knoppix floppyconfig

14. Test with PPP
Ctrl-Alt-F2 to switch to text console
wvdialconf /etc/wvdial.conf

Edit /etc/wvdial.conf; you should see:

[Dialer Defaults]
Modem = /dev/modem
Baud = 115200
Init1 = ATZ
Init2 = ATQ0 V1 E1 S0=0 &C1 &D2 +FCLASS=0
ISDN = 0
Modem Type = Analog Modem
; Phone = <Target Phone Number>
; Username = <Your Login Name>
; Password = <Your Password>

Add W3 to the Init2 string so we can determine connect speed
Uncomment Phone and Username; fill in appropriate values
Add an Ask Password = 1 line

aumix

Set PhoneIn volume to something much lower (25 is good)

wvdial

Once connected, Alt-F5 to switch back to X

To disconnect, Ctrl-Alt-F2 (pause) Ctrl-C (pause) Alt-F5