I had a similar problem when I first installed the new MC launcher. I had to keep removing it and installing it and eventually it worked.
I would make sure your Java is up-to-date and that old versions of Java are removed. Otherwise, maybe try to reinstall the launcher like BellStar03 said.
Yea, it seems since they went to the new launcher, things have been buggy for many people. What operating system/version do you have?
In my case, when I installed the new launcher it created a new Minecraft shortcut. I cound never get the new one to open. So what I did was go back to my original Minecraft shortcut and click on the highlighted part that said I was using an outdated launcher and that a new one was available. After doing that it indicated I had already installed the new launcher and asked if I wanted to remove it. I removed it and installed it again. There may be another may to re-install it that I am not aware of. And, like RatMazeMind said, I have had problems with my Java before. I have specificallly had problems after I have installed Java updates. For some reason it invariably installs 32 bit version and I have a 64 bit system. I didn't realize that was happening for a while, but, I couldn't get on Minecraft at all when that happened so now I watch for it.
Public Service Announcement: In most people's cases, you will not need to install Java yourself. When you download Minecraft from minecraft.net, it will automatically have the best version of Java available for your system and will install it for you.
Try uninstalling MineCraft itself and re-installing it. (When you buy minecraft, the account is what you pay for, not the game itself)
