I used Firefox, but I do have WinRAR. Should I try to uninstall it?
Edit: Odd, I created a new Windows user and downloaded the Launcher. The launcher itself doesn't work, but I can run the .jar now.
I'm having this same problem. I use 64-bit W7 and the latest Java. I have tried reinstalling both the Launcher and Java, but I'm still having this issue. My Windows username doesn't have anything but letters in it, so it shouldn't be the cause for this problem.