HTC Desire Z touch key number 2 (ABC) occassionally presses itself repeatedly without any apparent trigger. In such cases, I press the power button on/off to quieten it down. Is it a software or hardware problem. This happens infrequently but when it starts it is quite annoying as you cannot do anything with the keyboard as other keys do not respond to touch.
This is very likely to be a problem with the touchscfeen hardware. To test this, try installing a drawing/painting app from Google Play. Open the app, get into painting mode, and leave it for a minute. If you start getting paint appearing at the same point (where the 2 ABC soft key shows up), you know that part of the touchscreen isn't working. In the same way, try painting in the app and check whether any parts of the screen can't be painted on.
If there are any stuck parts of the screen, you can try giving them a wipe with a slightly damp, soapy cloth. Turn the phone off to do that, and make sure you dry the screen before trying to use it again. If that doesn't solve the problem, you're left with sending the phone back to the shop, or making a warranty claim, depending on how long you've had the problem.