Exchnage E-mail account delete button greyed out

I am unable to remove my university email exchange account from Mail app and I get a prompt box to input my password; the account is shut down now so I can't enter a password for it?

When I go into remove the account the delete button is greyed out.

This means I get dings to enter the password every 5 mins and the box pops onto the screen.

Help please!

[Re-Titled by Moderator]