You changed the kernel selection in your lilo.conf, but chances are you didn't change some of the other pointers there. Your System.map file can have an effect, as can the fact that you're pointing your lilo to one kernel, but loading up the rest of the system from another partition. The lilo man pages should help you figure out your specific problem, as can some of the docs at www.tldp.org
This is a normal problem for a newbie, and I'd love to tell you exactly what to fix, but not only do I think it would be better for you to learn this on your own, but you didn't post your lilo.conf
Just kidding. Mostly, lilo.conf setups are highly personalized, so it's best to get to know them well, as they are one of the most important parts of starting your system.
Also, are you absolutely sure that your winmodem is only supported by RH 7.1? Often driver pages lag distro versions, but kernels often can handle drivers in later versions. Not are they better tested, but occasionally a driver is added to the kernel, meaning your winmodem driver might already be supported without an extra driver. Usually the biggest problem is getting the info from the winmodem manufacturer. Once that's done, the work can be built on that base. (Somewhat unlikely with winmodems, but very possible, seeing as you have a driver for such an old version.)