Maybe the keypad or Security Module got fubar when battery changed, or wiring issue between the two just coincided with battery change. I would look at the wiring since it doesn't cost anything. Most likely place to look for damage is in the rubber boot between the driver's door and the body. You really have to look closely at the harness in there because there is a bunch of wires in it.

If you don't see anything obvious come back and I'll look in my 2002/2003 wiring diagrams for connector pinouts for you.