I'm putting this here because although dial out internet accounts may be on the wane, those of us that use them still deserve help.
I had lots of problems making a connection both in debian sarge (3.1) and very recently in Zen 1.2.3.
I did all the expected things i.e ran pppconf made sure my user was in dialout, but still a connection eluded me. I even, in desperation, changed permissions on /etc/ppp and /etc/chatscripts. Still no dice AND no connection. (Does it really need to be this hard when Mepis. Knoppix, Ubuntu along with other non-debian distros make it simple?)
Flame-away Debian-lovers!

The solution: from the Kppp Handbook http://gershwin.ens.fr/vdaniel/Doc-L...pp/kppp-7.html
This little gem worked! "Make sure that pppd is setuid root. You may set this mode by issuing chmod u+s pppd as root." e.g cd /usr/sbin then su and chmod u+s pppd
BTW there are lots of other answers to specific error messages at the kppp handbook and they could help whether or not you're using kppp to connect. ( I couldn't get Gnome's Modem Monitor to work either-before I issued that chmod command.

I guess the moral to this is READ The Manual but I'm still unconvinced that debian needs to make pppd set up so difficult.

is your module available in /dev/ directory

e.g modems make a module like /dev/ttySHSF0 to interact with the modem..is such a module there

where does your /dev/modem point to

if yes then are the permissions adequate

Yes the module is there. I put this post up to alert people to the problem with a few-not all debian distros. I see you list slackware as your distro-you will never have this problem in slack.
It's only debian and a few distros based on it the torment dialup/modem users. BTW I resolved the problem as-I stated in my 1st post by doing chmod u+s pppd.