Q: my screen wont respond to let me enter my password

Try:

- Reset the iOS device. Nothing will be lost

Reset iOS device: Hold down the On/Off button and the Home button at the same time for at

least ten seconds, until the Apple logo appears.

- Restore from backup. See:                                 

iOS: How to back up                             

Place the iOS device in Recovery Mode if necessary to allow the restore.

If recovery mode does not work try DFU mode.

How to put iPod touch / iPhone into DFU mode « Karthik's scribblings

- Restore to factory settings/new iOS device.

If still problem, make an appointment at the Genius Bar of an Apple store since it appears you have a hardware problem.

Apple Retail Store - Genius Bar