Okay, time for me to butt in here, Kirmonkey. You're obviously a little bit out of your league on this question. (Unfortunately for me, but) Fortunately for you, I've been down this road before. I'll try to wrap this question up for the most part here.
1. You have an internal (pci) winmodem
2. The manufacturer (conexant) has never released the hardware specifics for your brand of modem
3. Because of #2, there are no OpenSource drivers for your modem
Your options are this:
1. You can get zero cost ($0) drivers for your modem, but it will only run at 14.4K
2. You can buy the drivers for your modem ($20), and run at full speed 53.3k
3. You can buy another modem
If you decide to go with option #3, you can get a (external serial) hardware modem, or another software modem that has OSS drivers. A hardware modem would never require drivers and be the easiest to setup, but they tend to be a minimum of about $40. If you're interested in getting another software modem, I suggest the (Smart Link) sl-modem. There are OSS drivers for this software modem.
I've never used one of the sl-modems myself, but I have read good reviews about their ease of install. Here is one on ebay for only $5
In the end, you decision will probably come down to this:
1. If you want the modem to work RIGHT NOW! Then jump to http://www.linuxant.com/drivers
and buy the drivers.
2. If you're tight on cash and want the cheapest setup, a new sl-modem could be less expensive than buying the driver for conexant. (just watch the shipping rate though)
3. If you don't care about price and want the easiest setup from start to finish, then you'll want a (external serial) hardware modem.