Minecraft Demo Crashing

I have not bought minecraft yet. I was hoping to play the demo and then buy the full version after I was sure my computer would handle it well. I know I have the requirements and this is a new computer, but every time I login and pree "play demo," the launcher is hidden (like selected), the mojang screen pops up, and closes, taking me back to the launcher. The demo keeps crashing. I really love minecraft, but I'm wary to buy if I can't even play the demo.