I recently upgraded by kernel from the default 2.4.33 to the 2.6.18 kernel provided with the Slackware 11 install. Everything went fine except upon reboot by computer hung at getting an IP address from my DHCP server; it timed out and then continued loading.

Further investigation yields the following pattern of behavior:
Whatever NIC is plugged into the computer at the time of boot will be unable to obtain an IP address via DHCP. I have to get down underneath my desk and physically plug my cable into the other NIC. Once that's done, I can obtain an IP address normally. Only one of my NICs is recognized properly which is the 3Com Tornado. My onboard NIC is recognized as a Conexant unknown device but will operate with what I believe are generic drivers if I follow the above routine. I can change setting for both NICs via ifconfig, however, once I attempt to run dhcpcd the misbehaving NIC gets a "down" status according to ifconfig.

I guess I don't know where to even start troubleshooting for this and that's why I'm here.

Did you install the kernel modules for that kernel ? In '/testing/packages/linux-2.6.18' of install CD/DVD.

Yes, thanks for asking. I knew I was forgetting some detail when I posted. Yes, I installed the kernel, kernel source, and kernel modules but did not install the headers as advised.

Ok, so what Conexant card do you have ? I assume that 'lspci' says it is an unknown device, as you said earlier. That means there are no drivers for it available. So you must find the right driver module and install it. For that you need to know what card you have.

I'm sorry I took so long to reply, apparently what was dying wasn't my NICs but my router which took a nosedive right as I was replying. That being said, the NIC that hasn't been correctly detected is the onboard nVidia Gigabit ethernet.

Well, unfortunately, I have not found anything on how to get that NIC working. So it's just called 'nvidia gigabit ethernet', no model numbers or anything ?

I'm sorry my last reply didn't have enough information. I hunted down the driver CD for the mobo (I just moved so some stuff is still boxed up), and according to the README, it's a Broadcom NetXtreme Gigabit Ethernet controller. One imagines the next step would be to compile a kernel module for said card.

Yup, I believe the module is 'bnx2'. Check the kernel config to see if you have it. Also post the output of 'lsmod' to see if it isn't already loaded.