In Windows 10, the fix for the "hung" pop-up window for payment of state e-file charges is to go to Settings for display resolution and make sure it is at 100%. Many displays default to 125% or 150%. Restart TurboTax after you change the display to 100%. Then the "continue" button will work on the payment pop-up from the state e-file payment screen. Clicking on that will generate a pop-up to log into your Intuit account and pay.
There is a lot of bad information online about clearing cache and trying other browsers to overcome this problem with the state e-file payment pop-up. That makes no difference if you are running the program as a standalone download on your machine. Others suggest running TT as administrator (which you probably already are if you are the only user on your machine) and turning off your firewall temporarily. Neither of these worked for me. I can see that the software TT is using to generate the pop-up window was not being blocked by my firewall.
Similarly, for installation of the standalone TT program (where the screen for entering license information is blank), switch to the lowest resolution (600x800). Then you will be able to see the content of that screen.
It is clear many taxpayers have spent considerable hours trying to resolve both of these issues. Hope programmers fix these bugs soon.
