I set administrator password to blank. Now, I can't install new programs (message see in title), or change the admin password ("change" button grayed out). I tried a suggested fix from inside the terminal, but can't type anything into the sudo authentication field.
OK, there's two parts to this. First, to answer the question you asked:
Reboot into single user mode (see http://www.debuntu.org/recover-root-password-single-user-mode-and-grub if you don't know how) and set the password for root.
However, I don't think that will solve your actual problem. It sounds like the real problem is that the account you normally log in as is not a member of the sudo group - the root account on Ubuntu normally does not have a password, and is not allowed to log in directly. So, instead, I would recommend that you boot into single user mode as outlined above, then issue the following commands:
This will make sure that your user is allowed to become root, and will make sure that your user has a password which you can use when prompted. Once the machine finishes rebooting (the third command there), everything should be back to normal.
If you didn't ever set up a password you do not have to recover it but you just have to create it in System settings/User Account. There, click on Password.
So, let's create a new password that you will use as administrator for upgrading, installations and others. In few words, if you didn't ever create a password, create your password and use it when required.