Hi Bruce.
I'm a mac user for day-to-day computing , including PixInsight, and only use Windows in the observatory for hardware control so I only have a couple of other suggestions to try, if these don't work then I can't think of anything else.
Assuming you have not installed a third party AV / Firewall that has taken over your computer and you are using Windows Defender, carry out the steps below in the order they are written:
Step 1.
Open an elevated Command Prompt, to do this, type "CMD" (without the quotes) in the search box on the bottom tool bar of the Windows desktop.
In the "Best match" pop-up menu Right-Mouse-Click the item "Command Prompt App" and click on "Run as administrator"
In the UAC window that pops up "Do you want to allow this app to make changes to your device?" click "Yes".
Type the following command string in the Command Prompt Window at the flashing cursor, observing spaces, followed by the carriage return key:
netsh advfirewall reset
After the "Ok" response type exit at the cursor followed by the carriage return key.
Reboot the computer.
Step 2.
Click the Windows "Start" button, in the pop-up menu click "Settings" (the cog symbol).
In the Settings window click "Update and Security"
In the left side pane of the Windows Update window click "Windows Security"
In the right side pane of the Windows Security window click "Firewall and network protection"
In the right side pane of the Firewall and network protection window click "Restore firewalls to default"
A new window should appear after a few moments "Restore defaults" if it does not appear then it may be hiding behind the current window, check the lower desktop toolbar for the dialogues icon and click on it to bring the window to the front.
Click the "Restore defaults" button.
Click the warning message Restore Defaults Confirmation with "Yes"
Reboot the computer.
Step 3.
Open Microsoft Edge Browser
Click on the extras and commands menu, (three dots ... top-right)
Click the Settings button (cog symbol)
If not showing the full double-pane, click the left chevron symbol, <, top of the window
In the left side pane of the Settings menu click "Privacy and security" (padlock symbol)
In the right side pane of the Privacy and security window click "Choose what to clear"
In the Clear browsing data window select the following items:
Browsing history
Cookies and saved website data
Cached data and files
Tabs I've recently set aside or recently closed
Website permissions
Then click the "Clear" button
Exit all windows and reboot.
These actions should have reset Windows Defender Firewall Security and Edge Browser.
Now try launching PixInsight and completing the licensing registration, as you do so, watch the Windows desktop lower toolbar for Windows security pop-ups asking for your permission to allow the App (PixInsight) to access the internet, you must answer yes.
You will need to watch for that pop-up the first time you open a new app from now on until Windows firewall builds a new White list (Apps that are allowed internet access).
If PixInsight registration is successful then try reaching the previously blocked PixInsight forum pages in the Edge browser, hopefully this will be successful too.
Other than the above, I don't have any other ideas.
HTH
William.