You know some Internet lines were affected because of a weather storm, but you have not been able to access your e-mail all day long. Even now you are still unable to access your e-mail, yet you have been able to access the web, Facebook, etc. You have shut down your computer a few times.
You disconnected and re-connected your Internet modem. You can try clearing your DNS cache. In a command prompt type in "ipconfig /flushdns" without quotes.
Sometimes on Windows computers a local DNS cache is not flushed properly. This cache is supposed to get cleared when shutting down your Windows based operating system ie. Windows XP, Vista, Seven, Eight, Ten. Manually flushing your cache can potentially fix an issue where you cannot access certain Internet protocols.