Pavol, your English is much better than some native speakers I know, so that is not a problem.
The MD5 can read as good, but sometimes the burn may not. I have found it a good practice to burn at the lowest possible speed. Though, even with all the tricks, sometimes there are issues that happen.
If your hardware specifications are 64-bit, you may wish to consider installing that version. With Mint 6, there are some changes that my hardware did not like. I never had these problems with Mint 3, 4, or 5. I had bad luck with the 32-bit version of Mint 6. To even run the Live CD, I had to use "compatibility mode." However, the 64-bit version of Mint 6 installed without any problems, and it is running flawlessly right now.
With you getting as far as you have, you at least have narrowed down the "hardware detection" as the area where the whole installation quits. Sometimes the Ubiquity installer must be run a couple of times before it follows through to the finish. It boils down to my thoughts of you trying the 64-bit version.
If that does not work, you may want to make your own post with your progress up to that point. Your post at the end of this thread might not get as much notice as a brand new one. I hope you get up and running soon, but if not, there are plenty of folks in the forum who can give further suggestions. Good luck.