Apparently the original game and Brood War expansion are free to install through the Battle.Net launcher these days.

If you have the original discs, the later official patches added the ability to copy the "mpq" files from the CD into the game's directory, so you no longer need the disc in the drive. Of course, you're still going to need a drive for the initial installation. That should work for single player (it's been a few years since I last did it) but I don't know about online multiplayer.