Can I retrieve my saved files from the Minecraft demo by purchasing it?

I had the minecraft demo and it let me do whatever I wanted, its like I had the full version expect I couldn't play multiplayer. I had put a bunch of hours into the minecraft demo I had. I was playing on a kind of old PC (Windows 7) and it finally crashed. I lost everything on that computer. (including all of my saved games on minecraft) It made me really upset that I lost it all. Well, i've had a new computer for about a month and I downloaded the minecraft demo and its a different demo. You can only play five days and its over. Well, I tried to log into my account when I downloaded it. It said either log into account or start demo. I clicked log in and it sent me to a link that shows when I started that demo a few years back with all my saves on it (2011) and under username, it doesn't say my username, it just says username. I know this might be a little confusing but pretty much what i'm asking is, if I buy Minecraft under that same account, will I get everything from the demo back? Thank you so much for whoever answers this question with some good info!