I have an HP nx9010 working perfectly well with slack10.1.
The modem should be a conexant HSF. lspci says it is an Intel 537 chipset, but I've made several attempts to install such driver without success. Working drivers can be found here
/www.linuxant.com/drivers/
unfortunately not for free. A testing version limited to 14 K can be downloaded for free.
To be honest I must say linuxant service was very kind giving me a second license for free after some problems I had with my laptop mobo. Check first here
http://www.linux-laptop.net/
to have some useful compatibility infos about your laptop
Configuring you network is a simple task on slackware, just as root
/sbin/netconfig
and follow instructions.
A very good guide can be found here
http://www.slackbook.org/
Hope this helps
Ciao