Just so we're talking the same language, the 6270 is a "Touchcenter Keypad", usually referred to as a Touchpad, to distinguish it from Keypads. Touchpads have virtual keys while Keypads have physical keys to press. In Panel Programming, a Touchpad is called an "AUI" (Augmented User Interface, IIRC).
The actual
Control Panel (usually called the "
Panel") is a Printed Circuit Board (PCB) inside a steel cabinet, usually in some out-of-the-way place like an unfinished basement, utility closet/area, or hall or bedroom closet. The touchpads and keypads are interfaces between the Panel and the User. Think of them like the keyboard & screen for your computer not being the computer itself. There might be many touchpads & keypads in a system but only one Panel.
I'm pretty sure your Control Panel is a Vista-20P, even though the 6270 Touchpad is compatible with other Honeywell/Ademco models. AFAIK, ADT used only Vista-20Ps in homes in the era your system was installed. But it's always a good idea to name the model of the Control Panel (not just the Touchpad/Keypad) when you post asking for advice.
First thing to do when trouble problems with your Touchpad is to look at the manual,
http://library.ademconet.com/MWT/fs2/9/5910.pdf
with particular attention to Section 4 (Initial Setup) and Section 7 (Troubleshooting).
The first thing I'd try is to power-cycle the Panel (which powers down the Touchpad(s)/Keypads) by unplugging its power transformer and taking one wire off the Panel battery inside the steel cabinet. If you don't know where the Panel transformer is, you should find it. You ought to know where your alarm panel is plugged in--you might need to unplug it right away some day. It's a beige wall wart usually (not always) plugged into an outlet near the Panel.
After powering it down, wait 30 seconds and power it back up: Transformer first, then battery.
(And no, powering down the Panel doesn't erase any programming: Volatile memory was an '80s issue, for Ademco and most major brands.)
If power-cycling doesn't reset the sounds on your Touchpad, then it's time to study the Troubleshooting section of the manual. You'll need the Installer Code(IC), which ADT probably didn't tell you. ADT often used the same IC everywhere, but I can't tell you it because they get cranky with forum admins when somebody posts their IC on a public forum; but it's not hard to find. Google "ADT Installer Code" and you'll probably find it in a minute.
Let me know how it goes. Feedback helps.
EDIT: Btw, do you have any other keypads in your system?