The stormy weather wouldn't have affected your email password/login, so I wouldn't worry about that.
Who is your email with? - Are you able to check your login details with the provider? It may be worth checking your login details on another device and/or change your password and login on your phone again.
I'm sorry that you've been having trouble syncing some of your accounts.
It sounds like it may be an issue with your Google account, rather than your SIM. Have you tried reconnecting your Google account within your mobile's settings? As you've recently changed your password, you may find that certain apps etc need reauthorisation.