Does slackware 13 have any dependencies on a modular kernel? I am going to make the kernel without modules and wanted to know if this will not work or if it will be painful and still work.

Start with the generic config and just build in the modules you'd use if creating an initrd.

It's probably more dependant on your hardware than the Distribution.

Expect error messages. Many of Slackware's start-up scripts load specific modules. The following command should tell you which files need what:

I would also expect the autoprobing stages to complain if the modules aren't there (even if they're compiled into the kernel).

Unless things have changed go right ahead.
I haven't built a kernel on Slack for a while (certainly not on 13), but when I did I certainly would not have used modules.

And even if it all goes to hell, what have you lost ?. Even the time you spend doing it will be educational.

If I wanted to try, this is what I would do. You will need a recent kernel, at least 2.6.32.
- Run Slackware with a -generic kernel.
- Upgrade to at least 2.6.32.13, as of today (unless you run -current, of course) and keep the .config at the root of the kernel source tree
- Plug in all removable device you have (one at a time if you miss USB slots to do that), to make sure relevant modules be loaded. This include e.g. USB printer, scanner, camera, USB keyboards and mice, usb sticks, whatever. Don't forget USB hard disks.
- "make localyesconfig" in the kernel source tree (set-up localversion as -builtin for instance, to preserve modules you already have in /lib/modules) then make and install the kernel and the modules (if any), edit /etc/lilo.conf accordingly then run lilo.
- use it for some time to check that you don't miss any driver. If you do, add it with "make menuconfig", make and install again.

The goal of all that is having built-in only the drivers you do need, to avoid possible conflicts like the bad driver claiming some device at boot.

To know more: "make help" at the root of a recent kernel source tree

It's working fine. Just some complaints, as some have said, about modules on startup.
I noticed some alsa stuff trying to load modules. I think I can get this sorted out.

It most certainly is not.

I normally run a kernel with modules disabled and the drivers I need built in, and it works a treat.

Read Compiling your own Slackware Kernel

Everything's compiled fine, kernel seems to boot faster too.