Thanks for the responses.
Not exactly the same device, but this guide might help:
Actually, my device is detected and wvdial cdma gives me IP addresses and other stuff. Josh at the usb_modeswitch forum says there is some routing problem.
I had a similar problem. I solved by setting the DNS in /etc/resolv.conf.
So do you have to set the DNS every time you connect? I would rather not do that.
The same device works perfectly in Ubuntu. The only other significant difference is that in Ubuntu I have Gnome whereas in Slackware I have KDE. Should I try GSB with Slackware maybe?