Amazon systems won't work with a VPN in general since they are often used to try to hide someone's geographic location. Connecting to your router is your end of things on top of this. If it says your password is wrong, then likely your password is wrong.
Does your new router have the same name as the old one? As in "Fred's Wifi" when trying to connect? If so, something may be trying to use your old password. You might try resetting the Fire Stick but hang in there first, there's other people who hang out here far more experienced in Fire Stick stuff who might have better thougts than mine.
NOTE: I do NOT speak for or represent Amazon in any fashion. This is a customer to customer forum.
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