haenischr, it is a rare problem. I think that it is more likely to be a hardware problem unless it only happened after you updated the BIOS and never before.

It's time to try Dell Support. Put in your Service Tag and check on the warranty status of the system. Try the "Chat with technical support" option and start by telling them about the problem with the built-in keyboard and the relation, if any, to the BIOS update. Perhaps they have heard of this problem. Maybe there is a recall on it if it's not under warranty.