Hello jSfrmYYZ,
Being able to take a closer look at what's happening and getting more details about the steps you've already taken would be best in this situation, but I do have some ideas to get you started.
One of the reasons the button may be unresponsive is if you've already filed sales tax for that period. While it usually will bring up a message letting you know this, it's a good idea to make sure you're not trying to file for a period that's already been taken care of. Verify this by double checking the date range you've selected on the File Sales Tax window.
After assuring the dates are correct, check for data damage on the company file if you still can't proceed. Data damage can cause strange behaviours in the program such as this, so it's a good idea to double-check to make sure that's not the problem. Learn how to check for data damage here: Resolve data damage on your company file
If afterwards you're still having trouble or there are no errors found, get in touch with our phone support team so an agent can take a closer look. The number to dial is 1-877-772-9158 and QuickBooks Desktop Pro support is available 24/7. Intuit's support policies are outlined here: Intuit QuickBooks Desktop software support policies
Have a great week!