Deleted Exchange Password Prohibiting Access to IPad
Is it a wifi only iPad? If so, you can try to temporarily shutdown your wifi. If the iPad is not connected to Internet, maybe it won't try to fetch mails.

When you are prompted, have you tried to double click the home button and kill the Mail app? Or maybe try to access Settings from there.

You can also try to connect your iPad to your computer, if it's sync to iTunes. From there, in the Info view of the iPad on iTunes, select that you don't want any email account (I believe there is a overwrite current settings checkbox) and erase your accounts from there.
You'll probably have to re-add your others account manually.