"I'm thinking of putting a PCI card in my computer that gives me two new spots to hook up IDE cables."
I have used a secondary PCI controller for over two years. I highly recommend that you buy a HighPoint controller since it has by far the best Linux support.
"2) Would I have to compile extra drivers into the kernel to get this to function properly? I wouldn't imagine so, since it would be reading off of that hard drive to load the drivers, but one never knows...."
You need the drivers compiled into the kernel. The HighPoint drivers are distributed with the kernel and do not need to be added in a separate operation. This is not true of all IDE controler chipsets.
"The first two hard drives are Windows XP, and family is making them off-limits to Linux. So I'd have to have Linux on another hard drive. I don't know what this would make it, I'm guessing hde, but I don't know.... So I'm wondering, would it work to have Linux installed soley on that hard drive connected to the PCI card? I would have lilo as my boot manager (Since that's what comes with Slackware), so could it work? Or would I need something on hda (I might be able to have a tiny partition for my /boot if that's necessary, but I really wouldn't want to)."
You can put Linux on any drive that you want and it will work OK. The only thing that you have to do to /dev/hda is install the lilo bootloader on the /dev/hda MBR. When you get into the complexities of multi disk configuration I find grub a little easier to work with. I use grub on my MBR and lilo on my boot floppy.
"1) What name would the hard drive have? hde? sda?"
The 4 devices on the secondary controller are:
For what it is worth, here is my disk configuration:
/dev/hda is 120 Gig Seagate drive
/dev/hda1 is spare1 18G
/dev/hda2 is swap 2G
/dev/hda3 is / 19G
/dev/hda4 is spare2 82G
/dev/hdd is CD-RW
/dev/hde is 30 Mb Maxtor drive
/dev/hde1 is /makeCD 4G
/dev/hde2 is /home 1G
/dev/hde3 is /backup 10G
/dev/hde4 is spare3 13G
/dev/hdg is 40 Gig Maxtor drive
/dev/hdg1 is spare4 4G
/dev/hdg2 is /usr 9G
/dev/hdg3 is /software 9G
/dev/hdg4 is spare5 14G
Be prepared. Create a LifeBoat CD.