Try to run the game in "Admin Mode" or turn off your defender software.
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If you can see the Login page, it means you actually already connected to logindie.com. I guess your PC blocks the game from calling the browser, and I don't know why. The system is working well. Maybe you can try downloading the itch app version? (not OAuth version) Or you can visit our Discord and ask if anyone has met the same issue as you? :(