I have a 2003 Chrysler Town & Country and I just changed the battery. It now dings when the door is open with the lights off and keys out of the ignition. Whats wrong?

Changing the battery is probably just coincidence to the key warning.
The key warning alarm (ding, ding ding sound) is supposed to only happen when the key is left in the ignition and th e door is opened; to remind you to take the keys out.
However, over the passage of time, dirt can articulate in the key way and cause the warning switch inside to stick and cause the alarm.
Try this:

• With key out, tap or rap on the steering column with your hand. This might jar the switch loose (This is commonly referred to as "get a hammer" method-joking)
• Try spraying some silicone lubricant into the key way and working the key back and forth to see if this clears the switch.