Amount of free space on my computer:
Capacity: 499.76GB
Available 432.54GB
You are doing great on free space.
I tried to "repair disk partitions" but this didnt work, and everywhere I looked on the web it would say that this does not work.
It does work, but not for permissions issues on individual user files. It only has benefit on systemwide issues.
I also did a complete TimeMachine restore. This didnt work.
This is really only affective if you restore from a point in time when the issue did not occur which can be tough to know unless you try adding new Mail accounts every day.
_Go to Your User > Library > Preferences.
_Click on the Preferences folder once to highlight it.
_Go to File > Get Info
_Make sure that your user name is listed in the Sharing & Permissions window with Read & Write access
_Go to the bottom of the info window and click on the pad lock to unlock it
_Click on the cog / gear and then click on apply to enclosed items
_Now try adding an account in Mail again.
If the issue persists at this point it may be necessary to reset Mail which may require you to re-enter your account settings.
Remove Your User > Preferences > com.apple.mail.plist to the desktop and then open Mail and try adding an account.
Cheers.