Go up to HELP drop down menu in the top of the Blink window, look for the section on license management. If I remember correctly there should be two functions, one that lets you "transfer" your current license in blink and the other is an "update" your license. Choose the one that allows you to transfer it. If it asks if you want to remove it, say yes to the prompts. After you are done with that, go back into the license management and choose the "update" choice and reenter your current license key again.
Restart your computer and see if you have any problems after that. If you do, I would recommend going back to where you download Blink and briefly apply for another free license to be sent to you in email and then using that if you have to by doing the license update function again. Hopefully one of these things will help.