I'll just get straight to the whole thing. The main reason why you can't run this game today (when you hit play nothing happens and it shows you that you can hit play again) is because of Games for Windows – Live that died a long time ago. The easiest solution to this is by adding two files to the game main folder, my case would be: D:\SteamLibrary\steamapps\common\F1 2010

The two files are xlive.dll and xlive.ini

After you insert them in your game folder you can now run the game from steam without any issues. Check the next section to see additional info about graphics and some bug fixes regarding black screens and such.

Download link: https://files.fm/u/3sa5urftu
New link: https://easyupload.io/opm1cd

Also here is the video that I made which shows you how to do the whole process (the video is from my F1 2011 guide, but the process is exactly the same since both games used GFWL):


P.S IF THE DOWNLOAD LINK IS DEAD OR DOES NOT WORK FEEL FREE TO ADD ME OR COMMENT AND I WILL POST A NEW ONE.