My minecraft doesn't work, but my laptop is good!

I thougt that minecraft would work on my laptop. That laptop is very good and higher games then Minecraft works on that laptop too. I want to play Minecraft but I haven't enough money for it, so I play the Demo-Version.
I played the Demo-Version on an other computer and there worked minecraft perfectly! That computer was build in the year 2000 and have no upgrade on it! So why Minecraft don't work on my laptop?
It shows always the same:
"Uhoh, it looks like the game has crashed! Sorry for the inconvenience