Thank you all for your responses!
I'm afraid to say (for the sake of this thread), that I decided to clean install my PC. At first, I tried many
of the solutions on all the forums, like ipconfig that parman has just mentioned. Then I remembered, that some time ago I made permission changes to the registry. I used Process Monitor to check which keys read "ACCESS DENIED" when doing the "enable connection" operation and manually changed the permissions (everyone, full control) of all of those.
Even after all keys were unlocked, DHCP didn't work. My *Aaargh, the hell with it!* threshold was soon reached. Then I decided to do a clean install.
Again sorry, I hope you can understand it.. The good news is: everything is working now!