This happens to me as well, and my partner, with the added problem being that our wireless router kills the internet connection as well. We have been using the 'fix' posted here a while back by players of opening the game directory and launching the game using WoW.exe instead. That lets us login but every now and then it still shuts down our net. On those occasions, I have noticed that the game opens instantly but the cursor takes ages to appear in the text field. By the time it appears, I type in my password, it thinks for 2 minutes and then says I've been disconnected from the server. If I try to open the internet, there is no connection.
We need to restart our router so often its beyond crazy, and this results in us getting a new IP address each time, which has in turn resulted in our accounts being locked for suspicious activity, my partners once and mine twice, just in the 2-3 weeks since we came back to playing after a break.
For us, when starting the game as you normally would, the launcher appears, downloads a small amount of data, but only sometimes, and then we can hit Play as normal. The whole thing disappears and the computers appears to lock up briefly, the Windows hourglass appears, then nothing happens. If we check our Task Manager, Launcher.exe is there, but nothing ever opens. I have walked away for up to half an hour and come back and the game still hasn't launched. Without fail, everytime we try to use Launcher.exe, our internet connection is killed, and can't be recovered without a full router reset.
It sometimes happens with WoW.exe as well but not as often, so that is how we are logging in for now. I posted my own thread but haven't had any reply, I'm in Australia and missed Customer Service today as I had to go out for the morning.