As a backup plan I tried the LTS versions, which were successful. A friend of mine told me that the problem is a bug with Ubuntu that confuses the dvd drive if it is on a SATA3 port.
The solution is to plug the drive into SATA2 or IDE port.
I'm not sure, that this is the same problem that I'm experiencing as pendrive installs also failed, but in case of a DVD installation media it is worth a try.
The fact that you can't just unplug the DVD drive in case of a laptop further complicates matters, buit next time an external drive might be the solution.