Help solve the problem.
I bought the game, installed, I created an account and then an error crashes when starting:
the game could not connect to the authentication server
Yeah. You're in a forum section dedicated to a new game, not Elite Dangerous;
Suggest you start a new thread - with the same title - in the forum area, Chris gave you ;
https://forums.frontier.co.uk/forumdisplay.php/50-Elite-Support
This is also, the main support page, where Frontier are known to be very helpful and there known issues (and solutions) listed https://support.frontier.co.uk/kb/
Don't don't panic and you'll get it sorted. I'm able to run ED on a laptop nearly as old as the dinosaurs .. but initial set up can depend on circumstances.