I installed Slackware (once again) and this is what I get when starting up:

Verifying DMI Pool Data ........
Boot from ATAPI CD-DOM: Failure ...
Not found any [active partitions] in HDD
DISK BOOT FAILURE, INSERT SYSTEM DISK AND PRESS ENTER

When using cfdisk before installing I didn't choose that "boot"-thing on any of the partitions. The ones I have are:

hda1 - /
hda3 - /swap
hda2 - /boot
hdb1 - /home

And a third hard drive where the filesystem is FAT (this is where I saved all my important files before getting rid of Windows), I don't know what it's called but I guess it's hdc(?)

Could the problem be that I didn't choose "boot" on any?
Could it be that the third hard with FAT-system messes something up since I didn't install LILO (I'm not planning on using any other OS)?
Could it be because I chose the kernel bare.i/bzImage?

You didn't install lilo? Then what are you using?
It might be becasue you didn't set any partitions as active ('boot'), but I'm not sure.

Err, that was dumb of me. I read through the installation guide properly now and saw that I had read a part wrong. Thought it said that I didn't need LILO if I wasn't going to dual boot.

Just set lilo's timeout to zero or something to boot Linux immediately

I reinstalled everything and this time I installed LILO too.
Still wont' start though. I get the same message. I installed it to MBR and chose the right partition to boot. Seems like that wasn't the problem after all.

Anyway, I put in CD 2 and log in as root. Try startx but that doesn't work. I try xfree86setup, that doesn't work either. Lilo, lilo.conf doesn't do anything.

Is the bios booting from the right hd?
Isn't CD 2 the Live-CD? It is a small system that won't have a lot of the stuff like the hd one does. Use the first cd with the 'noinitrd root=/dev/hda1' option (assuming hda is the right disk) to boot your current install.

I looked in to the BIOS settings and changed from CD-Rom / C to C only.
Then I went into cfdisk and chose "boot" on hda1.

Starting up I get this:

An error ocurred during the root filesustem check.
You will now be given a chance to log into the
system in single user-mode ti fix the problem.

I then enter my root password and go into cfdisk where I put "boot" on hda1.
When starting up everything looks great and I finally thought it would work.
But I get that same message again. I try Ctrl-D which would apparently just go on but that doesn't work either. So all I can do is enter my root password and... well, do something.

It lets you log on in runlevel 1 (a sort of safe mode) to fix stuff. It appears to have not been shut down properly (because of other probs?), and you need to check the partition with e2fsck:
e2fsck /dev/hda1
You might need to do it with hda1 set as read-only if it isn't so already.
If it still has other problems, boot in runlevel 1 and try to go to runlevel 2, then 3:
init 2
init 3
See which runlevel has the problem.