Yup, modules always show up in lsmod.
Since this is a hardware problem "dmesg" is probably the first place where you should start looking (just type "dmesg"), before, after and when you try to use the modem. Since this is related to pppd deamon, /var/log/syslog could also give you some useful hints.
I don't quite understand the problem you had with the slackware kernel you compiled... If you want to try to compile a new kernel, there is plenty of howto online. The general line are :
1- Download a kernel (www.kernel.org
) and unpack it in /usr/src
2- Create a symlink (ln -s linux-x.y.z linux) so that /usr/src/linux point to your "new" kernel (it's how the system or packages then know which is your new kernel... it should always point to your actual kernel source, if you have any)
3- Enter the tree and configure the kernel ( "cd /usr/src/linux" then "make menuconfig" or "make xconfig" if you prefer). This is the critical step, if you forget this one, your new kernel will not have the correct options set.
4- Compile the kernel. On 2.6.X kernel, just type "make all" then "make modules_install"
5- Copy your new kernel image (from /usr/src/linux/arch/i386/boot/bzImage) somewhere ( usually /boot ) and edit your boot loader so it contains an entry about this new kernel. It is usually a bright idea to keep an entry about the old one, in case something goes wrong. Then you have to "reinstall" your boot loader on the mbr, as example if you use lilo, just type "lilo"
6- Reboot and test
The configuration file of the kernel is at "/usr/src/linux/.config". This file is the save of all your "options" so just copying this into a new kernel source directory is enought to tell "make menuconfig" what options you had. On 2.6.X kernel, you can also type "make oldconfig" before "make menuconfig" to let the make script locate the old config and try to create the new one from it. If your system doesn't have any /usr/src/linux (as most distro don't come with kernel source on default install because it is huuuge), there is usually a file in /boot named something like "config" which is a copy of "/usr/src/linux/.config".
In any case, if you want to try this, you better find a good howto on google as I skipped a lot of details.
Oh and **BIG FAT WARNING** --> Recompiling your kernel was just a suggestion, keep in mind you could (it could?) totally mess up your system doing so and it could not help at all. It is not very hard, but if you don't feel safe about it you maybe not want to try. This is some kind of disclaimer