I have a hard copy of the game, but with the CD it doesn't work, or even start. Plus it's not as convenient as having it on my laptop all the time. So is there a way I can download the full game since I own a copy?

No.

This would be considered piracy and a bannable offense from these forums. You'll have to make do with your CD of buy a new copy of the game. You can buy a digital version off Steam which doesn't require a disc.