According to many previous "solutions", the problem was on backward compatibility built in Win7, so advises were to check Winows XP compatybility for .exe files in game and to add administrator right to game files. Those weren't worked in my case.
It turned out that the only and ultimate solution is to change the paths in the Win registry. Smart guy who have found the problem and the solution says:
Today, through research and test, got the final solution (absolute playable) as below:link: Heroes 3 on Win 7 64 bit
The main reason is the registry file (11.reg, maybe other on your PC, but should be *.reg file) wrote HEROES III’s data to an improper registry location.
Open and compare 11.reg data and x64 Windows Registry, the modification method is obvious:
It can be seen clearly from the registry: all data of 32-bit programs are located at HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node, not located at HKEY_LOCAL_MACHINE\SOFTWARE directly.
This guy also has made registry file which changes this paths! link:Registry patch for Heroes 3
It means, you can make Heroes 3 playable in a few clicks. Just download a file, double click and play.