App store not recognising password

Sign out, reboot and sign in again.

Settings>iTunes and App Store>Apple ID

Try reset iPad a few more times.

Hold down the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears

Note: Data will not be affected.

Try update your apps manually.

App Store>Purchased>Look for apps that requires updating>Update manually

Check your date and time and Time Zone

Settings>General>Date and Time>Set Automatically>On

Update apps on iTune (computer) and sync to iPad.

Is your computer running the current version of iTunes 11.1.1?

Were the applications purchased with another Apple ID? Not sure? Right click on an app that won't update and 'get info'. This will show which Apple ID was used to purchase the app.

Are you unable to access the App Store on the iPad? (And therefore can't update or purchase from iPad). This is most likely a conflict between the ID and password in the settings and the valid ID you use.

Usually signing out Apple ID and signing in fixes it, but you tried that already.

Reset of settings may clear it. Reboot afterwards.

Update apps on iTune (tap to enlarge image)

Have tried 'Check for available downloads...' and it says "all purchases have been downloaded". Is there another way to Update the Apps in iTunes?

This doesn't update Apps.

To update Apps, on the computer, in your library, select 'Apps' from the left column. This shows all purchased apps.

Select update all from bottom of screen.

Check your settings on iPad in iTunes Store to see if auto update is off. ?? Otherwise they should update on request from the iPad. (More ios7 weirdness)