Starcraft – If I buy a SC2 digital copy from LA, will I be able to switch to the NA servers

According to a post by a Blizzard employee, you might be able to play with your friends no matter where they are:

Getting people online, playing and interacting is obviously the overall goal for the Battle.net platform, and that includes allowing people to play across regional boundaries as they have in the past.

Unfortunately, there are a multitude of challenges we have to overcome due to the unique regional account and billing options that didn't exist in the past. But those hurdles aren't insurmountable, and we are looking into solutions that will allow interested players to obtain access to other regional versions without having to buy another full copy of the game. Those solutions are something we're currently planning to have available through Battle.net Account Management within the first few months of StarCraft II's release.

Before that solution is implemented though, you're correct in that you'd need to purchase a US copy of the game on launch day to play in the US region.

However notice that he is talking about a potential future feature which may end up not getting implemented (or not implemented in a satisfying way), so in the meanwhile I would be careful about which version to buy.

If you still have the Starcraft 2 Disc all you need to do is install it onto the new computer like you did originally.

You do not have to uninstall the copy on your laptop, but you'll be unable to run starcraft 2 from both computers simultaneously (unless you're using offline mode).

If you have lost your starcraft 2 discs, you can install the game via digital download through battle.net, here: