How long has Starcraft been crashing on your system?
When the game crashes, do you get an error message? If so, what does it say (post its exact contents)?
What operating system are you using and what are your system specs?
Which hardware drivers did you update?
Does the game crash when starting single player games and when starting multiplayer games, or just one type of game (which one)?
Are you playing a particular map or maps when the game crashes? I played Starcraft recently, and I downloaded a Use Map Settings map that made the game crash to the desktop a few seconds after it started. Strangely enough, the crash only occurred in multiplayer...
If you've done all of the Blizzard steps for Starcraft crashes and you're still crashing, I'm not sure what else you should try, as the steps cover what I believe to be pretty much all of the main causes of crashes. Most likely the issue is software-related, as Starcraft isn't demanding at all hardware-wise and you can play all those modern games without any problems. Either it's a software issue, or it could be a serious hardware problem, although I highly doubt it. If the game started crashing only recently, we should focus on what things have happened with your system recently, both hardware and software-wise that could explain the problem.