My computer won't start. It goes to a black screen with a message saying that file system32/kernal missing? Can I use safe mode to fix this problem?

See if this helps:

http://support.microsoft.com/kb/307545

Yeah that would help but I don't have the disk to get in the recovery console. Can I do it without a disk?

I have another that pertains to another computer of mind. I have an another laptop and I can't get it to shutdown. It gets to the screen that says that windows is shutting down but it just freezes there. I would really appreciate some sort of arrow pointing me to the right direction.

The exact message is "<windows root>\system32\ntoskrnl.exe. What does that mean?

It means the computer cannot find your Operating System.

There is not much you can do without your XP CD or Recovery OEM CD if this was an OEM computer.