Each Apple program/app etc uses something called a preference list file- shortened to plist to configure it for when it opens. If one of them gets corrupted, then it can cause problems like the app not opening.
They are in the library. That will be extension .plist
For most problems like this, the trick is to find the plist file, delete it, reboot the machine and it will then compile a new one and usually the problem is solved.
Library is hidden so hold option then 'Go' in finder to reveal it. You may have to switch on hidden files or file extensions too.
I suggest you do a bit of searching to be comfortable with what you are doing and I suggest you search for mail .plist and it might tell you exactly what it's called and exactly where it is.
If you can open Mail and you still have problems, then go to 'window' in the toolbar>'connection doctor' for help.
Best
Ian