Touchscreen stops working after a few seconds on new iPad 2

The touch screen would stop working completely a few seconds after turning on. The iPad is still running fine -- Home/Power/Volume buttons work perfectly. But not the touch screen. I can not control the iPad except turning it on/off or turning the volume up/down.

Tried resetting the unit by holding Home and Power buttons. Still the same issue after rebooting.

Tried restoring the iPad completely from iTunes. With a clean iOS the touch screen still doesn't work.

Leaving the unit untouched for a few hours, then the touch screen would start working again.... for another few seconds. Then it stops working.

This is a replacement iPad which Apple Store gave me, but I'm out of the country now and there is no Apple Store where I am. How can I get this fixed?