Q: After Battery was switched out, the light in the Dashboard does not work anymore and the Trip Meters reset every time turn off

After Battery was switched out, the light in the Dashboard does not work anymore and the Trip Meters reset every time the engine is turned off. Tested fuzzes under dash and under hood, but all seem to be fine. Cannot see mileage or fuel gauge or temperature because of lack of lights - both day or night. Only view-able when using a flashlight. Odometer still works. Trip meters work when car is running, but then go back to zero when turning off the engine.

How can I fix it, where should I look? Who would be the best bet with a good answer? not just a bunch of guessing? (I went to a dealer and they did not have any quick answers - they were busy and I was travelling a long distance so there was not time for them to get into all the details and test everything) Seems like the dashboard was completely disconnected from power, yet warning lights still come on when expected as well as mileage is tracked and speedometer still works. Temp and gas gauges still work. So does the shift display

My car has 131000 miles.
My car has an automatic transmission.