What happens when you try to get email in the Mail app on it ? You've tried closing the Mail app via the iPad's multitasking bar and seeing if it works when you re-open the app, and/or tried a soft-reset ?
To close the Mail app via the taskbar :
iOS 7 : double-click the home button to open the taskbar, and then swipe or drag the Mail app's screen from there up and off the top of the screen to close it, and click the home button to close the taskbar.
iOS 6 and below : from the home screen (i.e. not with Mail 'open' on-screen) double-click the home button to bring up the taskbar, then press and hold any of the apps on the taskbar for a couple of seconds or so until they start shaking, then press the '-' in the top left of the Mail app to close it, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar.
Soft-reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.
And by 'Notes as a default' you mean ... ? If you mean in Settings > Notes then there needs to be a default place where new notes that you create on your iPad are stored.