Authentication is just the name and password of the WiFi you are trying to connect to.
Try 'forgetting' the info your tablet has on it for that WiFi. Then restart (turn it off and back on) the tablet and try connecting to the WiFi, which would require you input the correct WiFi name (if the WiFi is hidden) or choosing the correct name on the ones that show up. Then entering the correct password.
If you reset the modem, it is possible that the password was reset. So you need to check that as well.