The idea is to use the task manager once the black screen appears and the computer hangs. As you say, the computer is behaving normally before starting the game, but what is it doing at this point - is it repeatedly accessing the disc drive, or the internet, or has it posted a Windows error message hidden behind the black screen, or is the CPU busy doing nothing?
The update will certainly change some files, and stands a good chance of unblocking the problem, so please let us know what happens. And I hope you like it enough to buy it outright - I’ve been buying flight sims for about forty years, and of all the “games” I’ve had, the flight sims are always what I come back to, both for entertainment and education.