I also did some digging and found one of the solutions to the problem, although it only applies to nVidia cards, although the same functions should be available on Radeon as well.
The black border appears because the driver is not configured correctly.
The solution for nVidia is simple. Open the nVidia control panel, select the "Display" tab, then "Adjust desktop size and position," and check the box "Select scaling mode" - "Aspect ratio"
Now the game will stretch to fill the entire screen regardless of the resolution set.
Perhaps this information will be useful to someone with a widescreen HD monitor ;)
Added 5 minutes later
Guys, I need your help! I wrote about this yesterday: I'll reiterate the problem: I have a SONY VAIO Z690 computer, WIN 7, the disc is a licensed "gewel" version, I've done everything you suggested: I downloaded the patches, created "tdrLewel," checked the hosts file - but the game still won't start! My son's birthday is on Saturday - he's waiting for Heroes 6 as a gift! What should I do???!
MakStar, if your laptop has a video card with a burst mode (i.e., you have 2 video cards, Intel GMA and a switchable Nvidia/Radeon), you may simply not have activated the second card. The game simply won't run on GMA; you need to activate the second one.
If that doesn't help, try updating the video card driver to the latest version from the manufacturer's website.
If that doesn't help either, then the problem is most likely with the disc.