The DigitalOcean Console won't show the password as you type it in, so if you're not seeing anything show up when entering the password, this is normal. Simply type it in and hit enter. There's not a way to copy and paste, so typing it in is the only way.
If you've enabled SSH Keys on your Droplet, you may not be able to use Console as the
root user is not setup with a password, thus attempting to login through Console will fail.
You can try to contact support and see if they can help, though from my last conversation with them, they do not have any way to access your Droplet, thus they can't login and clear the block. This is even more so true if you're using SSH keys as they don't have your private key to use for authenticating with your public key.