After you reinstalled Windows, did you install the Intel Chipset Device Software? If not, install it now. There are other packages that you may need, most of which can be found at Dell Support page for your laptop.

Where did you try to adjust the brightness? Via function keys, or via Windows settings? 

To adjust it via Windows settings, Settings | System | Display | under Brightness and color, move the slider to adjust brightness for the laptop's onboard display.

To increase or decrease brightness via function keys, you may need to hold down the Fn key or not, depending whether you set priority to the standard function keys or to the additional icons and their behaviour on the function keys.

I tried to change both through the settings and through the Fn button, but nothing worked.
Regarding the Intel Chipset Device, can there be a problem after installing it, because I have a rather bad "relationship" with drivers)

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@RomanNNN wrote:
I tried to change both through the settings and through the Fn button, but nothing worked.
Regarding the Intel Chipset Device, can there be a problem after installing it, because I have a rather bad "relationship" with drivers)

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You need that chipset package installed. 

If you're worried, then before you install it you can create a new restore point in Windows, or use drive imaging software (e.g. Acronis or Macrium) to create a full disk image backup. I always do that before installing drivers or applications.