Is it possible to make a video game from your home computer

yes
http://www.microsoft.com/express/product/default.aspx to download. The C++ comes with a downloadable dark basic API just for making games. However you will have to learn how to program in C++ to make a game. Also you would need to be able to designed graphics unless you just want a text game. You can find C++ game making tutorials but they usally come in the form of text based games. You could also look up rpg maker xp or just rpg maker. They have easy to use programs to make games.