If the printer picks up other networks—in your case, not just the network settings, everything—the first thing I would do is do a full factory settings reset. ***If you have anything custom set, take notes of the changes, then rebuild. Some printers allow you to backup and restore, but that could cause the problem to come back in your case.*** If that doesn't work, see if it works over Ethernet as a test to make sure the networking is at least functional that way.
If the wireless is still not being detected after that and you've already checked the router connection and found nothing at fault, there's nothing in the Brother SM related to the wireless card that I can see that isn't risky or damaging to other critical data like the meter, S/N, and WIC count :-(. I tried—I found nothing. The only other option you could look into is resetting your router to factory settings, or if you have reserved IP addresses, dropping the reserved IP for your printer, letting it get a new one, and then re-reserving it. If it keeps having issues, the card may have been running on a silent failure for years that the power outage exposed when the power was cut and it lost the connection. It looks like Brother hasn't integrated anything in the maintenance mode to test the WLAN card or forcefully reset it back to factory when things like this occur.
Anyway here's the SM: [document|42104]