Winmodem is a term that refers to modems that let the operation system do some of the work for them. They are better called software modems, but because they are supported under windows and rarely and grudgingly under linux they are called winmodems. There are drivers for some of the software modems for linux and some are packaged live cd distros such as knoppix, kanotix, mepis etc.

The best place to see if a linux driver for your modem exists is : http://www.linmodems.org/

If possible, download and run the scanmodem tool found there, however if you can't open a root shell and type
Code:
lspci
and look for information about your modem in the output. You basically want to identify the chipset that powers the modem, and you can also open you pc case and eyeball the modem (if your eyes are better than mine) get some manufacturer names and numbers then consult the database at the linmidems site.
Another to id the modem is to K->sysem->info center and click on pci.

A couple of links for drivers for common chipsets:

Rockwell /Conexant
http://www.linuxant.com/drivers/modemident.php

Licent /Agere
http://www.heby.de/ltmodem

Good luck.