Screen brightness only works if I'm logged in with root, so it's obvious a problem of permission. The permission of what files do I need to modify in order to change screen brightness with a normal user? Or what other advice can you give me?

Thank you

There's not enough illumination in your post. Could you shed some light on what computer hardware and environment you have and what you are doing to try to set the brightness?

Also, a kitten dies whenever someone says "doesn't work". Please report exactly what happens. "Nothing happens" is a valid report. "The screen flashes but the brightness doesn't change" is also a valid report. "The system crashes" is a valid report. Note that "doesn't work" applies equally to these but is not helpful in pointing to the problem.

Ok, I am trying to modify it by changing the power profile. I simply try to adjust the brightness bar and it does nothing (the physical brightness doesn't change). There's no error. As I said before, this happens only with a normal user, but not with root, so it's obviously a problem related to permissions. I run 32-bit Slackware 13.37 on a laptop on KDE4. I don't think there's any need to display the laptop specifications. It's just a 8530p HP EliteBook, if you really think you need to know, but I don't see how this might affect the issue.

Now I've realised that I've made a mistake posting this thread here - by 'desktop' I understood 'graphic environment'. Meanwhile, I've found a solution on a another forum - I needed to add the 'power' group to my user and now it works. The problem now is that my shortcut keys don't work "fn" + "light up/down". A bar shows up in the lower centre of the screen, but that's all. It looks empty and it can't be modified at all when I press these keys.

Graphic environment is right, you are posting in the right place. The laptop type is important because X has to map function keys to those controls and different laptops have different keyboards. I see there's a kernel patch for similar HP laptops:

http://www.linlap.com/wiki/hp+elitebook+8540w

Unbelievable. I just added my laptop model in the line and it worked after reboot. I mean, it's dubious how it worked so easy, but even more dubious how linux didn't do it itself, as there is access to some sort of database from which information about laptop models can be extracted. So I'd have expected Linux to make the association itself, as there were some other HP models there written already. Well, all in all it's ok now and thanks for the link