Game not bought (Steam)

[nicoloconicolas]

Hi, I just bought TrackMania² Stadium on Steam (thanks to Steam sales), and I can't play it :c
I started the game, created an account and when I try to go on TrackMania² Stadium it tell me to buy the game.
I've seen thing about key on internet and I went on maniaplanet.com to try to register the key (which I found in regedit) but I've got an error :

Request ID: WU0BAn8AAAEAAGD@NIEAAADW
Date: June 23, 2017 11:52
Code: 500
Status: Internal Server Error

I also tried to register in the game (in the Key tab) and it tells me "Key registration failed.This game key requires Steam."
I don't what I've done wrong so I came here to ask for your help.
(Sorry if my English isn't good)