Mail crashed, won't respond.

I have a Macbook Air 13." Mail would neither open nor close a few days ago. Icon in dock had a dot under it, and command-tab showed Mail was open, but no window would appear. Days later, I tried force-quit, and the Mail icon disappeared from the dock. I tried to open it from "Applications" in the Hard Drive and a new icon appeared in the dock but the application still would not open a window. Now Maild does not appear in command-tab. Today I tried to restart my computer, but a window comes up saying that it can't restart because Mail is open.

Related circumstances: My Mail inbox had over 300 unread messages, as I read and respond to most email on my phone, and have been neglecting Mail on my laptop. On my laptop, I have numerous folders with saved emails that I would like to recover, relating to businesses and friends. Mail had been acting weird a few days before it crashed.