Thanks for the reply [NAME] , Happy new year. I've solved the problem using a Hirens BootCD. It allowed to execute the program in Windows environment and update the BIOS.  FYI, yes to all your questions (updated windows installer, etc...) Still, the motherboard doesn't recognize the 480GB SSD (ADATA). - It does recognize it in my newer Lenovo notebook.  I had to use this notebook's 240GB SSD (Kingston) in my Dell desktop though... Maybe I will open another question regarding this issue, though I am not sure if I want to go through 2 and probably more installations until it is solved...
Tried to install the BIOS update program via DOS prompt, but it doesn't work. After executing the .exe file, only replies with a message "Test." . Context: My SSD stopped working. Bought a new one (ADATA 480GB). BIOS doesn't recognize it. Windows Installation utility shows the new SSD, though is not able to create a partition larger than zero. I don´t have another way boot the computer and run the BIOS updater - as far as I know. I'm trying to update the BIOS in order to  be sure that it is not a computer problem or the SSD's problem.
BIO Update for Inspiron 5675