Thanks for reaching out to the Community. I'm here to help ensure to isolate the error you're getting so you can update your payroll version successfully.
If your computer can connect to the internet outside of QuickBooks Desktop but you're getting an error when updating payroll, let's process troubleshooting steps which is to configure Internet Explorer on your computer.
Before troubleshooting, you may want to try the task on another computer to see if it is successful and verify your network (if any) is compatible with QuickBooks.
Make sure you update to the latest version of Internet Explorer, IE 11, if you are using Internet Explorer 10 or or versions older.