Most pci modems are supported in Linux, at least for the 32bit distributions. The advice given by binary_y2k2 is extremely
bad advice. Go to
linmodems.org, do a little reading. There are two links on this page that you should check, one is called "archives", the other is called "scanModem tool". The later is a link to a script you can run which will produce all kinds of useful/useless information (depending whether the modem is supported or not), regarding your modem, where to get source code to compile drivers, what is needed to be installed to compile drivers, links to experts that can help you get it together if need be, instructions on howto, etc. etc. etc. If you have a Conexant modem, you're in luck because that's an easy one to get working, only problem with it is that it will cost you a couple bucks to get full speed, they only give you 1.4kps for the free version, but you'll be on-line in no time flat.
PS: I'm on dial-up also, it took quite a while to download the .pdf manual for the 5580 model (could not find a 5584), and the #@%$* thing wouldn't even tell me which model of modem it has.