Yes it is true.
initrd.img is used to start all of your program after your kernel start.
Some *Nix like OS don't force you to specified initrd.img, the kernel will locate it automatically, but Salck may be not that kind.
The sort of your disk is not a matter.
The initrd.img file is created when you install slack and I wonder if there is anyway to recreat it except extract from the slack install disk.
I dont' think that your initrd.img is corrupt, I think you just forget where it is.
And initrd.img is not the only thing you need to boot linux
you got this error
Code:
Kernel panic: VFS: Unable to mount root fs on 22:01
This mean your kernel couldn't start properly.
You have two more things to do with your grub.conf file.
Add the kernel parameter and specified the path to initrd.ing.
The easiest way to do so is read the lilo.conf file in your slack partition and adopt it.
I think your problem is not so serious
It is about the configuration failure not system failure