So I'm getting a new comp in about a week. I was wondering will it be possible to buy the game and play it today on my current computer and then, using the same copy, play on my new comp? Should I just wait? thanks.

i believe so i have it installed on my desktop and laptop

The game key is tied to your Battle.net account and not to a machine. So, I believe you can install the game as many times as you want on mutliple machines, you just have to log in with your account.

Yup, installing multiple times is a possibility.  You can even play the campaign as a "Guest" account so you don't have to sign into battle.net.

Blizzard is awesome and allows you to install it to as many computers as you want once it's tied to your Battle.Net account so yeah, totally possible.

yes we can!

do you need the disk in to play?

" do you need the disk in to play? "

And they save online your progress. Maybe only the save during one mission you can´t load in another computer. 

thanks guys